Turkish Prime Minister Recep Tayyip Erdogan and his UK counterpart Tony Blair have had talks in London on security, Cyprus and Turkey's EU bid.
Recep Tayyip Erdogan (left) and Tony Blair discussed Cyprus issue
Both leaders said they would work together against terrorism, after recent attacks in Turkey and the UK.
Mr Erdogan said the aim of terrorism was to set the West and Islam against each other, but they would not fall into that trap.
EU membership talks with Turkey are due to start in October.
The UK, which holds the presidency of the EU, has strongly supported Turkey's possible entry, raising concerns among other EU members.
Correspondents say the French and Dutch rejection of the EU referendum has dampened some enthusiasm for expansion.
The European Commission has said the October talks should be open-ended and Turkey will not be able to join until 2014 at the soonest. Turkey is also likely to face much stricter conditions for entry to the bloc than candidates in the past.
Before the membership talks can begin, Turkey must sign a protocol extending its customs union to the 10 new EU members, including Cyprus, a country it does not officially recognise.
Mr Erdogan said Turkey was ready for membership negotiations to begin in October as scheduled.
Mr Blair said he re-stated to the Turkish prime minister "very clearly" that the signing of the Ankara protocol ahead of the talks did not involve the recognition of Cyprus - as already made clear by the European Council in June.
He added that there were many uncertainties in Europe at the present time, but the prospect of Turkey's membership "will be important for Europe and for its security".
"I would like to congratulate the Turkish government and the prime minister for the great changes that have been made in Turkey over the past two to three years as a result of the focus of membership of the European Union," he said.
"Rather than seeing this as a concern for Europe... what it shows is the ability the European Union retains to be a powerful magnet for change and progress."
Mr Blair and Mr Erdogan also expressed condolences to each other over recent losses suffered in attacks by militants.
A Turkish citizen was killed in the London bombings of 7 July. A British holidaymaker was killed in a bombing a week later in Turkey, while tourists from both the UK and Turkey were killed in the weekend attacks on the Egyptian resort of Sharm al-Sheikh.