LONDON, Nov. 12— When Olympia & York Developments Ltd. decided in 1987 to undertake Canary Wharf, the biggest real estate development project in Europe, Paul Reichmann, the president of the family-owned company, said he was prepared to live through at least two downturns in the real estate market here.

The Toronto-based developer, which is staking nearly $:4 billion ($7.86 billion) on Canary Wharf, is now going through the first slump -- and without too much difficulty considering that London is in the grips of the worst real estate downturn since the mid-1970's.

As the complex of buildings at Canary Wharf steadily rises above the Isle of Dogs, 2.5 miles to the east of London's financial district, rents are falling and vacancies are climbing in central London. Several developers have filed for bankruptcy protection or have liquidated. Others are believed to be on the ropes.

There is more at stake here than the performance of Olympia & York, one of the largest developers of commercial real estate in New York. How the project fares will largely determine the merits of Prime Minister Margaret Thatcher's ambitious plan to revive the Docklands, the derelict area surrounding the wharf that in the heyday of the British empire was the home port for much of the country's vast merchant fleet.

Mr. Reichmann remains optimistic about Canary Wharf and the assumption on which it was built. He is still betting that London will remain the dominant financial center of Europe after the end of 1992, when the European Community plans to have eliminated trade and commercial barriers among its 12 member nations.

For now, Olympia & York is trying to line up tenants for the 4.5 million square feet of office space in the nine buildings that make up the first phase of Canary Wharf. In an effort to lay off some of its risks to banks, the company is also trying to refinance the first phase of the project.

When completed in 1997 or so, the 71-acre site will include 26 buildings, with 10 million square feet of office space; up to 500,000 square feet of stores, restaurants and other leisure facilities; a 400-bedroom hotel, and parking for 6,500 cars.

Eight of the nine buildings in the first phase, including an 800-foot tower that will be the tallest building in Britain, will be largely completed by mid-1991. Olympia & York says it has pre-leased 54 percent of the office space.

While "obviously I would be happier if 75 to 80 percent were pre-let, I'm hopefu it will be at that level next summer," said Michael Dennis, the Canadian who is chief executive of Olympia & York Canary Wharf Ltd.

Smaller tenants will begin to move in next summer. The first major one, Morgan Stanley, will follow in the fall. And Texaco plans to take up residence in the ninth building in mid-1992. A Change of Heart

Others that have signed leases include Credit Suisse First Boston, American Express, Manufacturers Hanover, London Wall Holdings, a big British insurer; Ogilvy & Mather, the ad agency, and The Daily Telegraph, the British newspaper.

Real estate experts are impressed with the leasing effort. "They are doing remarkably well," said Roger Nield, an executive at Chesterton, a major real estate agency.

But Olympia & York has also suffered some setbacks. Two big prospective tenants -- Merrill Lynch Europe Ltd. and Saatchi & Saatchi Company, the advertising giant -- changed their minds about Canary Wharf. The European Bank for Reconstruction and Economic Development, which is being created to finance the rebuilding of Eastern Europe, is not even considering Canary Wharf for its headquarters.

Olympia & York executives acknowledge having to offer juicy enticements to attract tenants. Analysts say these include assuming tenants' existing leases. Olympia & York even bought The Daily Telegraph's building in the South Quay section of the Docklands.

While Olympia & York did not get burned when it used similar tactics to woo companies to New York's World Financial Center in the 1980's, the moves increase its bet on the London market. Besides Canary Wharf, the company has joint ventures in other areas of the Docklands and owns sizable minority stakes in two big London developers, Stanhope Properties P.L.C. and Rosehaugh P.L.C. Disclosure on U.S. Portfolio

The first phase of Canary Wharf is expected to cost $:1.4 billion ($2.75 billion). So far, Olympia & York has invested more than $:800 million ($1.57 billion) from internal funds, bank credit lines or money borrowed against its North American properties.

Now, the company is negotiating with banks to replace that with money secured by Canary Wharf buildings. Mr. Dennis said Olympia & York was on the verge of completing a $:500 million ($982 million) general-project-financing deal and was beginning discussions about a $:600 million ($1.18 billion) loan secured by the tower.

The refinancing efforts, and the disclosure last month that Olympia & York was peddling a 20 percent stake in its United States real estate portfolio to outside investors, touched off speculation that the company needed cash for Canary Wharf. But Mr. Dennis insisted that Canary Wharf had no cash problems and said that the refinancing followed a timetable announced at the beginning of the project in 1987.

While banks have become more skittish about real estate lending, Mr. Dennis said they should lend to the project "given the extent of the equity we have in the project, the fact it is nearing completion and the extent of the leasing accomplished."

But Mr. Dennis said he will worry if Britain's interest rates do not drop sharply in the next few months. Vacancy Rate Up Sharply

The British Government cut its base interest rate in October to 14 percent from 15 percent. But further easing is unlikely soon.

As a result, real estate experts do not expect the London market to begin recovering before the end of 1991. And their forecast assumes that the Persian Gulf crisis does not result in a major disruption in oil supplies and a significant deepening of the shallow recession that economists believe Britain is entering.

The vacancy rate in the City, as the financial district is known, has risen to about 12 percent, from about 2 percent in 1986, and is expected to hit 15 percent or more this year or next.

Meanwhile, rents for new leases in central London have dropped by 8 to 15 percent this year. Those for new buildings in prime locations in the City have fallen to about $:55 ($108.05) a square foot, from about $:64 last year, said Simon P. Ward, a partner at Jones Lang Wootton, the real estate appraisers and brokers. "Significant growth in rents, by which I mean a 5 to 10 percent annual rate, is unlikely before 1993 at the earliest," he said.

Whether the slump seriously hurts Canary Wharf remains to be seen. The economic slowdown could provide an incentive for cost-conscious companies to move there. Thanks to low land costs and Government tax breaks, Olympia & York can charge rents of $:27 to $:30 ($53.04 to $58.95) a square foot -- about two-thirds the typical rent in the City. Modern Quarters

In addition, Canary Wharf's buildings will be state of the art in everything from air-conditioing to their capability to house computer and telecommunications systems. The same cannot be said about much of the office space in central London: 45 percent predates World War II, 31 percent was built between the war and 1979 and 24 percent after that, according to Jones Lang Wootton.

This lack of modern office space was a major reason Paul Reichmann and his two brothers were willing to undertake a project as big as Canary Wharf. With a unified Europe bringing increasing competition and opportunities to the area, Mr. Reichmann argues, companies will become increasingly willing to move out of central London into these kind of quarters.

But the Reichmanns also decided that for Canary Wharf to compete with central London, it had to be a stand-alone business center.

In addition to the shops, offices and hotels, the plan calls for Canary Wharf to offer a transportation system that is vastly superior to London's, with roads, subways, a light railway, a catamaran river bus service on the Thames and proximity to two nearby airports. Olympia & York is contributing at least $:500 million ($982 million) to help pay for all this. And the British Government has pledged $:3 billion ($5.89 billion).

Real estate experts say that once these plans are completed, Canary Wharf -- and the Docklands -- will flourish. But that may not be until the mid- to late 1990's. In the meantime, Olympia & York faces the formidable task of wooing corporations to an area that looks more like a construction site than a place of work and that can be a nightmare to reach. No Rush to the Top

Although the first trees will be planted next month, many of the basic improvements and the expansions of the transportation system will not be completed until the end of 1992 or early 1993. And Olympia & York does not expect the extension of London's subway to Canary Wharf to be completed before the first half of 1996.

"Obviously we moved faster than the Government agencies working on various transportation improvements, who are trailing us by about a year," Mr. Dennis said.

Despite the challenges, he does not sound worried. Indeed, he seems in no rush to rent the top floors of the tower. While most of the deals in the tower have averaged about $:30 (58.95) a square foot, he says the top section should command at least $:10 ($19.65) more. "If we opened and had the top quarter of the tower left, it wouldn't dismay me at all," he said.

Nor does he consider the pullouts by Merrill Lynch and Saatchi & Saatchi to be a bad omen. Analysts agree, noting that both have suffered financial setbacks and are retrenching.

Yet even those real estate experts who are impressed by progress say it is not clear whether Olympia & York will make money on Canary Wharf. "It's far too early to tell," said John J. S. Coventry, a partner at Hillier Parker May & Rowden, a property agent and consulting firm.

Mr. Dennis says he has no doubts. "We expect the first phase to be a financial success and not to have to wait 10 years as some have suggested," he said.

Photos: The 50-story Canary Wharf Tower, right, the tallest building in Britain, dwarfs other buildings under construction in Olympia & York's Canary Wharf development project in London's Docklands area. (Associated Press); Map: Canary Wharf, London (pg. D1); Paul Reichmann, president of family-owned Olympia & York Developments Ltd. (Peter Redman/Financial Post) (pg. D21)