Since he took over the Trafalgar Studios, director Jamie Lloyd has staged some of the most thrilling and accessible productions of Shakespeare I've ever seen. And it's all been done with an eye to keeping the bard as accessible as possible. There are low ticket prices for young audiences. And with A-listers taking on title roles such as James McAvoy's Macbeth or, in this case, Martin Freeman as Richard III, Shakespeare has never been cooler.

This production even looks cool. For the '70s conference-room set, designer Soutra Gilmour appears to have raided London's swankier retro furniture stores.

Richard and his ever-dwindling entourage enter and exit via two lifts positioned on either side of the stage. It is a set that belongs to the Wilson era, we are told in the programme.

It was a time of intrigue and paranoia (mainly Wilson's) about dark establishment forces that were out to get him. It turns out he was right. But the real intrigue here is in the casting of Freeman.

He's an actor whose best known roles - Tim in The Office, Bilbo Baggins in The Hobbit movies and Dr Watson in Sherlock - exude decency. And that's because casting directors surely sense in Freeman that very quality.

Less convincing are this Richard's powers of seduction

So it is fascinating to see how, casting against type - despite his latest role as the worm who turns in the TV version of Fargo - Freeman handles Richard's bloodlust and ambition.

It is never an uninteresting performance. Brimful of irony, Richard's most ruthless moments are accompanied by a knowing sheepishness, as if crimes such as the strangling of Lady Anne with a telephone cord were on a par with double-parking.

Making light of heinous murder is this Richard's signature. But less convincing are this Richard's powers of seduction. And when he seduces Anne in the company of the body of her husband he murdered, there's just not enough charisma to believe that Anne could be won over while in the depths of grief and at the height of her hatred for Gloucester.

It is less of a problem with Gina Campbell's poised Queen Elizabeth because this mass murderer, who is more Harold Shipman than dagger-wielding Duke, can get his way through the more traditional means of blackmail and threat.

There are false steps elsewhere in Lloyd's otherwise engaging production. Jo Stone-Fewings as a public school Buckingham is terrific up to the scene he publicly breaks down Richard's fake reluctance to take the throne. English reserve gives way to the persuasive powers of a gospel preacher at full evangelical throttle.

This may well have worked for a Richard III set in Texas but not for one that is meant to recall 1970s London during the Winter of Discontent.

And while I can see the temptation to link Richard's opening line with that period of strikes and strife, it's hard to transpose this king's barbarity to a time best known for the bins not being emptied.