A committee of MPs has backed Turkey to join the EU but warned issues around human rights and the conflict over Cyprus must be resolved first.
The Foreign Affairs Select Committee visited Turkey and found itself "struck by the country's economic dynamism and international ambition".
But chairman Richard Ottaway said elements of the Turkish judicial system were troubling. The stalemate in Cyprus has effectively left the country's process of joining the EU "stuck", the committee report adds.
Despite the problems, the cross party select committee endorsed the UK's continuing relationship with Turkey being based on an accession process.
Launching the report, Mr Ottaway said: "When we visited Turkey, like many visitors we were struck by the country's economic dynamism and international ambition.
"But we were also taken aback by much of what we heard about Turkish legal proceedings and practices, which did not seem to us to ensure the kinds of human rights standards that we would want to see from a country that we want to see inside the EU.
"We are pleased that the Turkish government seems to be aware of the shortcomings and to be taking some steps to improve matters.
"We recommend that the Foreign and Commonwealth Office (FCO) should seek every opportunity to help Turkey in practical ways to achieve further improvements in its human rights practices, including as regards freedom of expression and the media."
The report said one of these measures could be to make it easier for Turkish nationals, especially frequent visitors, to get an entry visa to Britain.
It said: "The UK's visa regime for Turkish nationals is one of the greatest obstacles to the development of closer UK-Turkey ties.
"The regime undermines the credibility of the Government's wish for a 'strategic partnership' with Turkey, as well as being a significant practical and psychological obstacle to intensified relations.
"The FCO should explore possibilities to make the acquisition of UK entry visas easier for Turkish nationals, especially frequent visitors."
An FCO spokesman said: "The Foreign and Commonwealth Office welcomes the recognition given in the report of Turkey's growing political and economic role on the world stage, and its analysis of ways to strengthen the UK-Turkey relationship.
"We also welcome the Committee's endorsement of the Government's steadfast support for Turkey's EU accession, as an important element of the bilateral relationship.
"We believe that Turkish accession would be to the wider benefit of the UK and EU, contributing to our prosperity, security and stability.
"Turkey has made clear its firm strategic commitment to accession to the EU, and successive European Councils have made clear that Turkey is a candidate for full membership of the EU.
"The UK is working closely with the Turkish Government, both bilaterally and with the EU to prepare Turkey for accession to the EU. In 2011/12, we have offered technical assistance on a range of issues, including freedom of expression, women's rights, and judicial and public administration reform.
"We welcome the Committee's recognition of the strength of UK-Turkey ties.
"We work closely with Turkey on foreign policy issues critical to UK interests including Syria, the Iran nuclear issue, Somalia, Afghanistan and the Western Balkans.
"The Prime Minister has committed to doubling bilateral trade with Turkey over the next five years. Total trade reached £9.1 billion in 2011 - an increase of 40% since 2009.
"The Government is committed to building on this success by raising awareness of market opportunities in Turkey amongst UK exporters, and tackling outstanding market access issues.
"The Committee has highlighted a number of concerns on human rights, particularly freedom of expression.
"We share the concerns expressed by the European Commission about Turkey's human rights record, and we encourage the Turkish Government to take further steps to encourage greater freedom of expression particularly in the media. We welcome recent steps taken by the Turkish Government to reform its judicial system and look forward to further progress.
"The Committee also raised the Cyprus settlement negotiations, where we are committed to supporting the UN's efforts to achieve a settlement based on a bizonal, bicommunal federation with political equality."