Their last meeting was in Ankara, this time it is London, and top of the agenda for British Prime Minister, Tony Blair and Turkey’s Recep Tayyip Erdogan, is Turkey’s hopes of joining the EU.
Afterwards, Ankara is expected to sign a customs union protocol.
It is the last hurdle to membership talks and will open Turkey’s trade borders to the 10 countries that joined Europe last year.
Turkey has already introduced a number of reforms to its judiciary system and its human and minority rights legislation.
This latest protocol is of particular significance however as it refers specifically to Cyprus.
Ankara has made it clear it does not see the signing of the treaty as any kind of recognition of the Greek Cypriot government.
Turkey recognises only a breakaway Turkish Cypriot enclave in the north of the Mediterranean island and so far international efforts to resolve the dispute have come to nothing.
Recognition of Cyprus is not a prerequisite for starting entry talks. Negotiations could begin in October, despite reservations by many current members. However it is likely to be a decade or more before a final decision is taken.