The announcement comes during the Prime Minister’s one-day visit to the Turkish capital Ankara, where she became the first Western leader to meet president Recep Tayyip Erdogan since last year’s attempted coup.
Mrs May told the president that Britain stood with his defence of Turkey’s democracy, but warned him it was “important” for him to uphold human rights.
Speaking to Mr Erdogan as they addressed the press at his presidential palace, Mrs May said: “Turkey is one of the UK’s oldest friends, our relations stretch back over 400 years but there is much that we can do in the future to build on that relationship together.
“I’m proud the UK stood with you on July 15 last year in defence of your democracy. Now it’s important that Turkey sustains that democracy by maintaining the rule of law and upholding its international human rights obligations, as the government has undertaken to do.”
Mrs May had come under pressure to raise human rights issues with the Turkish president, who has imposed a state of emergency involving waves of arrests, the closure of numerous media outlets and the removal of thousands of public officials - including judges, academics and teachers - from their jobs.
Speaking before the PM’s arrival in Turkey, Amnesty International’s UK director Kate Allen said the visit was a “vital opportunity” for Mrs May to ask “probing questions” about allegations of excessive use of force and ill-treatment of detainees by Mr Erdogan’s security forces.
The human rights situation in Turkey had “deteriorated markedly” during the state of emergency imposed after last July’s botched coup, said Amnesty.
Mrs May and Mr Erdogan also discussed counter-terrorism, security, trade and migration in talks which stretched for an hour longer than scheduled.
During the visit, the UK-based BAE Systems and Turkish Aerospace Industries signed a Heads of Agreement document establishing a partnership for the continued development of the Turkish Fighter Programme (TF-X).
British officials said the contract would safeguard high-skill jobs at BAE Systems and could lead to opportunities worth billions of pounds over the lifetime of the project, with potential future contracts to provide engines, weapons, radars and sensors.
It was hoped the deal would pave the way for a deeper defence partnership, effectively making the UK Turkey’s partner of choice for key aerospace technology.
Mrs May, who has made preparations for closer post-Brexit trading links her top priority for the Turkey trip, said: “This agreement underlines once again that Britain is a great, global, trading nation and that we are open for business.
“It marks the start of a new and deeper trading relationship with Turkey and will potentially secure British and Turkish jobs and prosperity for decades to come.”
BAE Systems chief executive Ian King added: “The announcement signals an exciting next step in relations between both Turkey and the UK with the co-operation between BAE Systems and TAI paving the way for a deeper defence partnership.
“The agreement confirms ongoing collaborative work on the design and development of the aircraft.”
The contract was announced by Mrs May with Turkish PM Benali Yildirim, following talks at his ministry building. The pair also signed an agreement on aviation security.