Can Great Britain still make a splash without headline star Billie Piper?

Although transfers from subsidised or smaller theatres to the West End obviously involve financial risk, producers gamble that the first run has proved the demand for a particular show or star and that reviews or word of mouth from the original can be used to draw other punters in.

But in the case of two shows moving to commercial venues this month, the flutter is greater because the show now being sold is not quite the one that original audiences saw. In the Theatre Royal Haymarket production of Richard Bean's newspaper and police farce Great Britain, the main role of a red-top editor passes from Billie Piper to Lucy Punch, while for the transfer to the Vaudeville theatre of the musical revue Forbidden Broadway, one of the startlingly versatile cast of four, Sophie-Louise Dann, has been replaced by Christina Bianco.

In both cases, the reason for recasting is not the unhappy one of unsuitability or creative differences but the happiest one of being too much in demand: Piper had a prior commitment to the TV drama Penny Dreadful and Dann to the musical Made in Dagenham. And each show still has a lot going for it without the one who has gone. However, the switches illuminate a delicate aspect of theatre production: whether and when the success of a show becomes inseparable from a particular actor.

This decision is becoming more frequent. The interest of TV and movie stars in making theatre appearances brings short-term gains – the whole run of a show starring Nicole Kidman, Benedict Cumberbatch or Jude Law will sell out quickly – but long-term loss, as the screen fame that shifts the tickets means that the actor will soon be required back before the cameras, preventing extensions to meet ticket demand. There would have been little point in employing replacements for Kidman in The Blue Room, Cumberbatch and Jonny Lee Miller in Frankenstein or Law in Henry V, because so much of the buzz around the productions was prompted by their involvement.

So producers dream of a show becoming such a brand that it can live on long beyond the loss of a lead player; what might be called the Doctor Who model. There was considerable scepticism in the industry about the prospects of One Man, Two Guvnors without the astonishing central performance by James Corden in the premiere staging. Commercial producers favour major stars, which is why, to Alan Ayckbourn's frustration, the plays he premieres in Scarborough have routinely been recast for London.

However, One Man, Two Guvnors flourished in the West End and on tour with a succession of substitutes including Rufus Hound, Owain Arthur and Gavin Spokes. It seems likely that the National has drawn on that experience in backing the post-Piper prospects of Great Britain, director Nicholas Hytner and dramatist Richard Bean's first collaboration since One Man, Two Guvnors. The creator of a role, though, inevitably casts a shadow: as often happens, the actors chosen to replace Corden and Piper are physically similar to the original.

The dilemma of whether a play can be separated from its first star was well illustrated by two of the productions that stand alongside One Man, Two Guvnors in the lists of the most successful new plays ever staged at the National: Peter Shaffer's Amadeus (1979) and David Hare's and Howard Brenton's Pravda (1985). In each case, ticket sales were driven by a spectacular turn from one of the greatest stage actors of the day: Paul Scofield as the possible Mozart-murderer Salieri and Anthony Hopkins as the mock-Murdochian newspaper tycoon Lambert Le Roux.

Both shows had long and lucrative runs at the National but Scofield, who liked to spend as much time as possible with his family and garden in Sussex, and Hopkins, who was finding theatre progressively less satisfying, declined to take the roles to either the West End or Broadway.

Although later audiences were unfortunate to have missed Scofield – as we were reminded by a film clip of his rendition in the recent televised National Theatre 50th birthday gala – the production continued to prosper with Frank Finlay's Salieri in London and Ian McKellen (followed by many others, including John Wood and Frank Langella) in New York. Pravda, however, stopped when Hopkins did, although a magnificent Le Roux from Ralph Fiennes in one of the live sections of the NT 50th birthday event suggested that a suitable understudy for Sir Anthony may now have been found.

In the 80s, producers were more cautious about recasting – and one star more reluctant to take over a role stamped by another – and, if current judgements had been applied, it is likely that Pravda would have continued with another heavyweight (John Thaw, Michael Gambon) in the part.

Even so, even now, some roles defy recasting. It would have been a brave – and possibly career-suicidal – actor who had agreed to take over from Helen Mirren as the Queen in Peter Morgan's The Audience, as Mirren had established a divine right to portray Elizabeth II with her work in the earlier Morgan film The Queen.

But, although Bean's Great Britain seems unlikely to reproduce the huge profitability of One Man, Two Guvnors, it does seem to replicate that play in being a vehicle that can be driven by more than one pair of hands, while Forbidden Broadway is an ensemble piece that can be played by any quartet of multi-talented actors. Viewers of the first productions are unlikely, though, to refrain from bragging to later admirers that the original casts were better.