The stars of the BBC’s Sherlock, an adaptation of Sir Arthur Conan Doyle’s Sherlock Holmes mysteries, have downplayed suggestions of a homosexual relationship between the principal characters.

Benedict Cumberbatch plays the title character in the BAFTA-winning production, the second series of which began on New Year’s Day.

He said: “Much as Sherlock adores John, and he’s fond of him, there’s no love, there’s nothing sexual – all the jokes aside.”

“The problem is, [jokes] fuel the fantasy of the few into flames for the many. People presume that’s what it is, but it’s not.”

Martin Freeman, who plays his companion Dr John Watson, said: “There are a lot of people hoping that our characters are rampantly at it. If you want to think that they are secretly at it, then you can, but we’ve never played anything like that.”

Mark Gatiss, co-creator of the series, said: “We’ve had lots of fun with the notion that, in the 21st century, people naturally assume they are a couple.

“The stuff that people really enjoy is the relationship between them. The banter and the rows and the proper feeling between them, which really leaps off the screen.”

The series was met with some criticism in the media and on Twitter for its depiction of a nude dominatrix before the 9pm watershed.

But a BBC spokesman said: “We’re delighted with the critical and audience response to the first episode, which has been extremely positive, and have received no complaints at this stage.”

In 2010, Robert Downey Jr, who plays Holmes in the current film versions, discussed the homoerotic tension between the two characters, who were shown wrestling and sharing a bed in the first film of that series.

He said he wondered whether Holmes was “a very butch homosexual”.

The holder of the US rights, Andrew Plunkett, told Total Film: “I hope this is just an example of Mr Downey’s black sense of humour. It would be drastic, but I would withdraw permission for more films to be made if they feel that is a theme they wish to bring out in the future.

“I am not hostile to homosexuals, but I am to anyone who is not true to the spirit of the books.”

A 180% rise in the sale of Sherlock Holmes literature was reported while the first BBC series was being aired, and the sandwich bar below the setting for the sleuth’s flat at 221B Baker Street said it enjoyed a surge in business from fans of the show.