Riding high after his enormous success in London and New York as Jerusalem’s Rooster Byron, Mark Rylance returns to Shakespeare’s Globe — the London theatre he ran for ten years till 2005 — with a mesmerising portrait of the stage’s most gleefully unrepentant badhat, Richard III. This is another bravura performance in which, as with the amazing Rooster, Rylance shows a man behaving madly and disgracefully while successfully persuading us to like him for it.

The pantomimic nature of his villainy is evident from the outset. He leers and preens his way through the famous first speech, laying bare his plan to prove the villain with evident confidence we might not recognise him actually to be the thing, or at any rate not to mind much if we do. Thus it is. Once he has lied and murdered his way to the throne, the Globe audience assumes the role he expects of us and cheers the new king to the rafters (not that this roofless Wooden O possesses any).

Gloriously caparisoned in stripy yellow (lavish Jacobean costumes are a feature of this good-looking production — designer Jenny Tiramani), he is not the bottled spider of a Crookback that Antony Sher showed us but a nasty wasp always eager to sting. Rarely has so comic a Richard been seen, much of the humour arising from his and our shared recognition of the huge gap between his’ words — “’Tis death to me to be in enmity” — and his deeds.

Those foolish enough to trust him learn their mistake too late to save them from their fate — first brother Clarence (Liam Brennan), next Hastings (Paul Chahidi) and then the self-serving accomplice to his scheming, Buckingham (Roger Lloyd Pack). To these victims are added, most famously, the young Princes in the Tower, portrayed most spiritedly and touchingly on Press night by Austin Moulton and Lorenzo Allchurch.

Generally, it is the women who have his measure, especially his deeply disillusioned mother, the Duchess of York (James Garnon) In the case of Lady Anne (Johnny Flynn) this does not prevent her accepting Richard’s outrageous proposal of marriage delivered over the corpse of her father-in-law, whom he has killed. Politics wins out over the heart here, as it does when Queen Elizabeth (Samuel Barnett), the mother of the slaughtered princes, agrees to support Richard’s marriage proposal with her daughter. All three of these women, it will be noted, are played by men, always entertainingly, if (understandably) not very convincingly. With much use of stirring music (composer Claire van Kampen) and ending with the Globe’s trademark dancing by the whole cast, the production (director Tim Carroll) continues till October 13 (box office: 020 7401 9919 — www.shakespearesglobe.com).