“Was Shakespeare a Fraud?” Roland Emmerich’s rollicking costume drama Anonymous depicts Shakespeare as merely the over sexed and ill-educated front man for the real literary genius of the age — Edward de Vere, 17th Earl of Oxford. If you care about historical accuracy you’re probably better off with Dr David Starkey’s slavering descriptions of 16th-century power broking and savagery. In this ripping yarn the only skewerings are of a literary nature.

Like the Bard himself, Anonymous is blessed with a surfeit of plots. Skipping between the reign of the young Queen Elizabeth I (Joely Richardson) and the elderly Good Queen Bess (Vanessa Redgrave) it’s best approached with a clear head as well as an open mind. On one level there’s the theatrical triangle involving playwright Ben Jonson (Sebastian Armesto), nobleman Edward de Vere (Rhys Ifans) and the opportunist thespian William Shakespeare (Rafe Spall). Jonson is the man de Vere initially entrusts with producing his manuscripts and keeping secret the true identity of “Anonymous”. But Shakespeare rumbles their scheme, blackmails de Vere and turns himself into the most celebrated author in 16th-century London.

A parallel storyline beginning 40 years earlier shows how de Vere as a boy first delighted Queen Elizabeth with his juvenile writings. As a youth (played by Jamie Campbell Bower) he grows up in the household of the Queen’s adviser William Cecil (David Thewlis) before marrying his daughter Anne and embarking on a torrid affair with the Virgin Queen. Out of this come various illegitimate children, financial problems for de Vere, scheming over the succession to the throne and — most important — a lot of plays.

You’d expect the director behind blockbusters like Independence Day and The Day after Tomorrow to put on a good spectacle. I don’t much like the obvious fakery of the CGI that now dominates every period evocation of London. (The snowy funeral scenes towards the end were particularly unimpressive.) But the costumes and sets are magnificent as Anonymous moves at dizzying speed between court intrigues, romance and the theatrical spectacles that delighted and inflamed Elizabethan London. Audiences back then didn’t just sit politely applauding — sometimes they jumped on stage and got stuck in. As the charlatan Shakespeare, Rafe Spall often seems to be channelling the spirit of Sid James, with his broad comic interpretation of the character.

In this ripping yarn the only skewerings are of a literary nature.

If this had been a Carry On film then the role of de Vere’s disapproving wife Anne would surely have been played by a screeching Joan Sims — “Edward, you’ve been writing again!” — rather than the austere Helen Baxendale. But this film shows de Vere’s problems as a lot more complex than simply having a wife who didn’t understand his genius. I won’t spoil the surprises, but by the end de Vere emerges as the most tragic character in Anonymous. Ifans’s measured performance conveys all the inner turmoil of a man whose compulsion to keep writing sees him betray his family, his class and his Queen.

Edward Hogg is also impressive as the scheming Robert Cecil, resisting the urge to make this hunchback into another puritanical pantomime villain. I think it’s fair to say that Redgrave and Richardson give us a portrait of Elizabeth that emphasises libido over political astuteness. But like everyone else — from Trystan Gravelle’s odious Kit Marlowe to David Thewlis’s statesmanlike William Cecil — they look as though they had a ball making this film.

Some people have a problem with the whole concept of Anonymous and the liberties it takes with history. But if Showtime can get away with the dubious mix of sex, violence and wooden acting in The Tudors, I really don’t have a problem with a film that sets out to do more than titillate. Anonymous celebrates the enduring brilliance of Shakespeare’s work — whoever wrote it.