Turkey should become an EU member state despite refusing to recognise Cyprus, UK Foreign Secretary Jack Straw said.
Mr Straw was critical of free speech rules in Turkey
Mr Straw believes its entry into the union would be a blow to those who say there is a "clash of civilisations" between the Muslim world and the West.
"It will prove that a secular democracy which shows respect for Islam can live comfortably in Europe," he said.
Talks on its entry bid are to begin on 3 October but there is opposition to full membership in several EU states.
Turkey recently issued a declaration reaffirming its refusal to accept the Cypriot government, which effectively only controls the Greek part of the Mediterranean island.
Mr Straw said: "Acknowledging that Turkey's declaration raises genuine concerns - which we, as presidency, are working hard to address - does not mean that we should delay the start of Turkey's historic accession negotiations."
The foreign secretary went on to tell the Institute of Public Policy Research in London that Turkey's membership of the EU was of "paramount importance" for the future of the union.
He said: "Turkey is a secular nation with a majority Muslim population.
"By welcoming Turkey we will demonstrate that Western and Islamic cultures can thrive together as partners in the modern world - the alternative is too terrible to contemplate."
Turkey has ongoing disputes with several EU members and senior politicians in France and Germany have voiced doubts over its entry.
These doubts were strengthened when many voters in France and the Netherlands cited fears about Turkey as a contributing factor in their decision to reject the EU constitution.
The country's human rights record has also been called into question and Mr Straw admitted there was "still some way to go" on the implementation of measures to protect freedom of speech.
The October talks on Turkey's entry bid will take place in Luxembourg.
The UK took over the EU's rotating presidency for six months on 1 July.