Russia's President Vladimir Putin will hold talks with UK Prime Minister Tony Blair at Downing Street on the second day of his UK visit.
Trade is also set to be on the agenda, with Mr Blair saying the two countries' economic futures are bound together.
Mr Putin will also present awards to the British crew who took part in the rescue effort in August to save a team of Russians trapped in a submarine.
It is over two years since President Putin last visited Downing Street.
Since then there has been "somewhat of a chill" in relations between the UK and Russia, said the BBC diplomatic correspondent Bridget Kendall.
The Kremlin reacted angrily when British courts refused Russia's request to extradite two outspoken critics of the Russian government, the prominent Chechen separatist, Ahmed Zakayev and wealthy Russian businessman Boris Berezovsky, before granting them political asylum.
But now, "it seems both sides want to put aside their differences", our correspondent said, reports BBC.
According to Independent, Tony Blair said the two sides had discussed the Chechnya conflict during the EU-Russia summit talks. But he and Mr Putin made it clear at a news conference that economic relations were becoming the core of the relationship.
"We want to work to take the relationship between Europe and Russia to a new and more intense and strengthened level," Mr Blair said. " This is a relationship in economic terms that can only grow and prosper and strengthen."
At home, Mr Putin's stock is high as the world's largest country luxuriates in record oil prices, enjoys an unusual period of political stability and holds its head high on the world stage.
The fact that the Kremlin's control of the economy and the media is getting tighter is of little concern to ordinary Russians. Their prime concern is their quality of life, and Mr Putin appears to have understood that, repeatedly telling his 144 million fellow Russians that raising living standards on the back of a strong economy is his priority.
With his approval rating at around 70 per cent, no real challenger to his power has emerged and the opposition remains weak. Most Russians would like Mr Putin to stand for a third term in 2008 when presidential elections are held, regardless of the constitution limiting him to two terms. P.T.