It’s a not a mission for the faint-hearted: rescue a script in serious need of humour and writerly panache. But if anyone can do it, Fleabag can.

Phoebe Waller-Bridge, who created, wrote and starred in the eponymous BBC hit, has been brought in to liven up the script of the next James Bond film, still known as Bond 25.

She has been specifically requested by Daniel Craig, who plays 007, to bring her wit and quirkiness to the screenplay, the Observer has learned.

Craig, who lives in New York with his wife Rachel Weisz, is a fan of Fleabag, which reached the end of its second and probably last series on BBC1 last Monday, and also of Killing Eve, which Waller-Bridge developed.

Waller-Bridge has been in New York for the past few weeks, latterly performing in a stage version of Fleabag, which ends on Sunday.

Sources close to the film in the US said that while in the country she discussed with Craig how to improve the script of Bond 25, which the 007 actor felt needed some “polishing”, by introducing more humour and the offbeat style of writing she is best known for.

Daniel Craig as James Bond. Photograph: Allstar/United Artists

Bond 25 has been hit by problems ever since it was announced four years ago. Initially, Craig said he would rather “slash my wrists” than play the spy again. But he relented, possibly due to the many millions on offer, just over a year ago. However, Sam Mendes refused to direct more Bond films, and in 2017 Danny Boyle was brought in along with John Hodge as screenwriter. Boyle, who was also in charge of the opening ceremony of the London Olympic Games, knew Craig from the Bond spoof they had concocted there with the Queen.

But Boyle left Bond 25 in August, citing “creative differences”. Within a few weeks, the American Cary Joji Fukunaga, who had made a handful of well-reviewed films, was hired as his replacement. The writing duo of Neil Purvis and Robert Wade, who had penned several previous Bond movies, came on board to re-work what Hodge had started. There have long been rumours that Bond 25 might be based on the novel Never Dream of Dying by the US author Raymond Benson, which featured Bond as a spy.

Then, in February, a third writer, Scott Z Burns, best known for his screenplay for The Bourne Ultimatum, was brought in before Waller-Bridge. All this has meant that filming has been delayed repeatedly and that the original release date of October 2018 was not met.

Until quite recently, it was hoped that Bond 25 (the latest rumour is that it will be called Eclipse) might be released in October this year, but that date has now been pushed back, first to February 2020, and now April next year.

Filming proper has still not begun despite some pre-production work on locations in Italy, Norway and Jamaica, plus Pinewood in the UK.

In the meantime, Craig is in New York, having recently filmed a thriller, Knives Out, while Ben Whishaw, who will play Q again, has recently said he has not seen a script. Ralph Fiennes will reprise his role as M and Naomie Harris will again be Miss Moneypenny. The latest rumours are that Rami Malik, who recently won an Oscar for his Freddie Mercury, could play the evil Blofeld.

So far, then, the setting up of Bond 25 has witnessed as many twists, turns and spills as any 007 film. On the assumption that Craig, along with long-time producers Barbara Broccoli and Michael G Wilson, are happy with the final script, Bond 25 should start filming within a fortnight.

Before Waller-Bridge, there has only ever been one female writer – the Irish-born Johanna Harwood, who had been secretary to Harry Saltzman, the first Bond producer along with Albert Broccoli (Barbara’s late father). Saltzman then brought Harwood in to help with the screenplay of their first film, Dr No, and for the second, From Russia With Love.

Neither Eon Productions, which produce the Bond films, nor representatives of Waller-Bridge in the US, responded.

Craig’s agent in the US said: “I’m not the guy to talk of rumours.”