Afghan President Hamid Karzai is in the UK to discuss the departure of British forces with PM David Cameron.
The leaders will sign an agreement setting out how their two countries will work together after UK combat troops withdraw in 2014.
Britain is set to build a military academy in Afghanistan, based on Sandhurst
The meeting follows France’s announcement that it is bringing forward its troop withdrawal by one year, to the end of 2013.
Mr Karzai said in Paris on Friday that Afghan troops would replace the French.
He said: “France and other allied countries have helped Afghanistan considerably in the past 10 years.
“Afghanistan, because of that help, is now ready to take more and more responsibility.”
The BBC’s world affairs correspondent, David Loyn, says Britain has twice as many troops in Afghanistan as any other European nation but not enough to fill the gap left by the French.
Mr Karzai will meet the prime minister at his official country residence, Chequers, in Buckinghamshire.
The UK will be the third stop comes after Mr Karzai visited Italy and France.
Our correspondent says Mr Karzai will brief Mr Cameron on the state of peace talks with the Taliban, which are just starting.
Mr Cameron is expected to sign an agreement to build an officer training college in Afghanistan, based on the British Army’s Royal Military Academy at Sandhurst.
The agreement will also commit Britain to continue providing aid support for Afghanistan after British combat troops withdraw.
Mr Sarkozy announcement came after the deaths of four French soldiers in Kapisa province.
France currently has about 3,600 soldiers in Afghanistan.
Paris wants to bring home 1,000 of its soldiers this year, with only a few hundred left after 2013.
In a survey published on Thursday, 84% of French people said they supported the full withdrawal of troops by the end of this year.
Mr Sarkozy’s Socialist opponent in this year’s presidential elections, Francois Hollande, has pledged to bring troops home this year if elected.