During a speech Tuesday, Russian President Vladimir Putin asserted that the West should respect “the free will of Crimeans” to secede from Ukraine and join Russia. (Ruptly.TV)

To President Vladimir Putin, Russian billionaires are a vital constituency in a state built on cronyism and kleptocracy.

To London’s luxury property dealers and high-flying bankers, the oligarchs play a different but no less exalted role: free-spending customers willing to shell out gobs of cash for everything from fine Mayfair estates to elite soccer clubs.

Relations between Moscow and Europe may be at their lowest ebb in a generation, but the two sides share a common reliance on Russian high rollers.

It’s a dependency that makes Putin vulnerable if the West decides to get serious about sanctions in the coming days. Yet it also means European leaders are less likely to do so for fear of damaging their own fragile economies. To alienate the oligarchs might mean pricking the property bubble in Moscow-on-Thames, as London is sometimes known.

“At almost every level, this is a city in thrall to Russian money,” said Jonathan Eyal, who directs international security studies at the Royal United Services Institute. “We should be able to withstand Russian blackmail. But we can’t seem to resist the sight of suitcases filled with cash.”

That issue is at the heart of Russia’s showdown with the West this week, after Putin and his aides laughed off an initial round of sanctions against a handful of officials and pressed ahead with the annexation of Crimea.

The West’s seeming inability to influence Putin has prompted soul-searching across Europe over whether the continent is putting its commercial interests ahead of its security. Although similar discussions are underway in the United States, the ties with Russia run much deeper here — and the stakes are far higher.

A senior member of Britain’s ruling Conservative Party, Malcolm Rifkind, on Tuesday described the European response as “pathetic” and compared it to the appeasement of Germany on the eve of World War II.

“It can’t just be putting token penalties on a few individuals,” Rifkind, who chairs Parliament’s intelligence and security committee, told the BBC. “It has to be very robust financial sanctions.”

European Union officials are weighing just such a move and are likely to announce additional penalties this week. But any union-wide measures require the agreement of all 28 members, many of which are reluctant to do anything that would cause long-term damage to ties with Moscow.

British Prime Minister David Cameron on Wednesday urged his fellow European leaders to adopt tough sanctions when they meet in Brussels beginning Thursday. On Tuesday, Britain moved unilaterally to suspend all military relations with Russia and halt arms deals, with Foreign Secretary William Hague telling Parliament, “We should be ready to contemplate a new state of relations between Russia and the West in the coming years that is different from the last 20 years.”

Yet the very existence of those arms deals reflects the changed nature of Russia’s relations with Western Europe since the last time tensions ran this high, during the Cold War. Back then, the two sides were hermetically sealed from each other, with little crossover of money or men.

That began to change after the 1991 breakup of the Soviet Union. But it is only in the Putin era of the past 15 years that the distinction between Russian and European economic interests began to blur.

Now their economies are so deeply entangled that Russia and Britain share the same wealthiest man: iron and telecom magnate Alisher Usmanov, who is reported to be worth $22 billion and maintains lavish homes in both countries.

Evidence of Russian extravagance is all over London: the $200,000 bottle on offer at a Russian wine shop; the vodka-and-caviar restaurants that have become the toughest reservations in town; the Russian accents in the halls of the priciest prep schools.

Elsewhere in Europe, the connections are just as thorny. Germany, for instance, imports a third of its natural gas from Russia. Although its leaders have talked hopefully of cultivating alternative sources — including imports from the Persian Gulf region or even the United States — the reality is that any solution that doesn’t involve Russia is many frosty winters away, analysts say.

France, meanwhile, has a $1.7 billion arms deal with the Russian military and is due to deliver a spanking new warship, the Vladivostok, this fall.

But it is in Britain where the Russian connection is in many ways most conspicuous.

Oligarchs have flocked here for the few-questions-asked banking laws, the top-flight schools, the convenient air connections back to Moscow, and the vast networks of goods and services that cater to the super-rich.

Alina Blinova is part of those networks, having co-founded a concierge company serving those with extravagant means. She said she helps her clients with “day-to-day lifestyle” issues such as finding a home, a chauffeur or a private jet.

“Whatever the client asks us, we make their dreams come true,” she said.

Blinova was recently featured on a reality television show called “Meet the Russians” that was described by one reviewer as “brilliant escapism at its most opulent.”

But in general, most wealthy Russians have eschewed the spotlight here, taking pleasure in the lack of attention they draw compared to life back home in Russia.

Among the central appeals to life here, in fact, are the litigant-friendly libel laws, which help to reduce the specter of public scrutiny. The banking rules, too, allow would-be-customers to open accounts without disclosing much about the source of their assets — a key criterion for anyone who’s carting around misbegotten funds.

While some wealthy Russians have run afoul of Putin’s regime and moved to the United Kingdom to escape his wrath, many maintain warm relations with Moscow, and are here to hedge their bets.

“It’s a relatively safe bet to park your money in London,” Dominic Grace, head of London residential development at Savills, a real estate agency. “We still make foreign money pretty welcome here on the whole.”

Sergei Guriev, an economist who left Russia under pressure from the government last year and who now teaches in Paris, said there are enough Putin associates with financial interests in the West that U.S. and E.U. sanctions could have a significant impact if properly targeted. “You’re in big trouble if you’re on these lists,” he said. “You can’t travel. Your friends and family will have their reputations hurt. It’s not what you want in a globalized world.”

But that same globalized world also demands open markets and borders for the well-heeled. To suggest otherwise could mean London loses out.

“We need to be willing to harm ourselves to harm Russia,” said Andrew Foxall, director of Russian studies at the London-based Henry Jackson Society. “We’re long past the point where Western financial centers should be enabling Russian kleptocrats. But that’s undoubtedly what’s happening.”

Karla Adam contributed to this report.