A small group of Ukrainian protesters with posters reading "NATO Save Ukraine" awaited Kerry as he arrived at Downing Street for a meeting with Britain's Prime Minister David Cameron and Foreign Secretary William Hague ahead of his talks with Lavrov.
Cameron underlined the threat of sanctions when he sat down with Kerry, telling him that "we want to see progress as much as you do."
"We want to see Ukrainians and the Russians talking to each other. And if they don't then there are going to have to be consequences," he added.
Kerry thanked his British hosts for their strong position, saying that "we're all hoping that we don't get pushed into a place where we have to do all this. But we'll see what happens."
European and U.S. leaders have repeatedly urged Moscow to pull back its troops in Crimea, and stop encouraging local militias there that are hyping up the vote as a choice between re-joining generations of ties with Russia or return to echoes of fascism from Ukraine's dark World War II era, when some residents cooperated with the Nazi occupiers.
Western officials instead have asked Russia to start diplomatic talks with Kiev as a way of de-escalating the tensions.
But the Crimea vote seemed all but a done deal — and experts said it would almost certainly result in breaking away from Ukraine.
Kerry told a Senate panel on Thursday that he planned to make clear how high the stakes are when he sees Lavrov in London. He suggested he would press Russia to accept "something short of a full annexation" of Crimea — but did not elaborate on what that might entail.
"There will be a response of some kind of the referendum itself and, in addition, if there is no sign of any capacity to be able to move forward and resolve this issue, there will be a very serious series of steps on Monday in Europe and here," Kerry told senators.
"My hope is that they will come aware of the fact that the international community is really strong and united on this issue," he said.
His comments echoed those of German Chancellor Angela Merkel, who hours earlier said Russia risks "massive" political and economic consequences if it refuses to soften its stance against the new government in Kiev.
The showdown has been cast as a struggle for the future of Ukraine, a country with the size and population similar to France, which is caught between its long-standing ties and traditions with Russia and more progressive and economic opportunities in the West. Twice in as many months, Russia has moved thousands of troops to its border with Ukraine that U.S. officials have described as an intimidation tactic cloaked as a military exercise.
It was not clear, however, whether Russia would heed the warnings, and Moscow has refused demands by the West to pull back troops from Crimea and respect Ukraine's territorial boundaries. Under a long-standing security agreement with Ukraine, Russia is allowed to deploy up to 25,000 troops to the Crimean Peninsula, and has a large navy there.
"There are limits on how much blunt force, in terms of sanctions and isolation, will move somebody who doesn't seem to have been particularly responsive to that throughout his career," said John Norris, a security expert at the liberal-leaning Center for American Progress think-tank in Washington. He was referring to Russian President Vladimir Putin.
Kerry and Lavrov have spoken almost daily as the Ukraine crisis has unfolded but have yet to find any common ground.
At the Senate hearing, Kerry said Moscow should expect the U.S. and European Union to take measures against it on Monday if Russia accepts and acts on a decision by Crimea to secede from Ukraine. The U.S. and EU say the vote Sunday violates Ukraine's constitution and international law. Russia has said it will respect the results of the referendum.
In another show of support for Ukraine's sovereignty, U.S. Vice President Joe Biden met with Ukrainian Prime Minister Arseniy Yatsenyuk on Thursday, a day after the new prime minister met with President Barack Obama. The White House said Biden told Yatsenyuk that the U.S. "stands firmly behind Ukraine and the Ukrainian people in ensuring Ukraine's sovereignty and territorial integrity."
Obama has imposed limited sanctions against unidentified Russian officials thought by the U.S. to be directly involved in destabilizing Ukraine.
But Congress on Thursday put off a vote that would have expanded those sanctions, as well as approve $1 billion in loan guarantees to Ukraine and International Monetary Fund revisions to help Kiev. The Senate won't vote on the measure until March 24 at the earliest, when lawmakers return from a weeklong recess, while House Republicans are pushing their own Ukraine aid bill that includes no Russia sanctions or IMF provisions.
Sen. John McCain sharply criticized fellow Republicans for not acting "when the people of Ukraine are crying out for our help." He said he'd never been more embarrassed by members of his own party.
"Don't call yourself Reagan Republicans," McCain said. "Ronald Reagan would never let this kind of aggression go unresponded to by the American people and we're not talking about troops on the ground. We are talking about responses that impose sanctions and punishment for Vladimir Putin."