When the phrase 'Roman comedy' is used, it's hard not to spring immediately to thoughts of Up Pompeii!. And indeed, there are distinct whiffs of Frankie Howerd in this knockabout romp of Roman silliness, not least in the central conceit of the sly servant outwitting the self-important master.

To be fair, the threads of comedic influence spread further and wider than simply plundering the 1969 sitcom. Overtly billed as inspired by the plays of Plautus, it lifts its main plot from the ancient author while simultaneously claiming to be 'lovingly ripped off' from the source material. That tagline hints at another significant reference point: Monty Python.

But there are also echoes of Moliere, Feydeau and even Blackadder and Richard Bean in the supremely daft script by Phil Porter, who delivers classic farce characters in a setting that is both refreshing and resonant. So General Braggadocio, the pompous narcissist gulled by the superior wits of his slave, is given to pontificating in words that might come direct from the Twitter feed of Donald J Trump, while one stunning set-piece of witty wordplay relies on a grocery delivery by a certain Ocadus.

Some of the bells of recognition ring louder and more heavy-handedly than others, but the heart of this show is always in the right place. Under the directorial care of Janice Honeyman and with a relentlessly chuckle-inducing musical score full of sousaphones and banjoes from Sam Kenyon, it never takes itself too seriously and is always anticipating the next laugh.

Occasionally, there's a sense that everyone's trying just a bit too hard, and some of the broad comedy lands more successfully than others, but the ensemble constantly feel as if they're fully behind the intent of the show, doing their utmost to deliver a rollicking night of freewheeling fun.

In this, they emphatically succeed. Sophia Nomvete plays the crafty slave Dexter as a loveable rogue with a ready wit and plenty of schemes. She's energetic, alert and utterly focused for the full two and a half hours. Felix Hayes as the over-the-top general is straight out of the Graham Chapman school of authority nitwits, while one-time 'Allo 'Allo star Kim Hartman makes an entertaining cameo as an ageing prostitute roped in to assist the devious doings.

Honeyman's sensitive handling of the farcical elements is complemented by a beautiful set design from Colin Richmond, evoking ancient Rome in exquisitely drawn detail, while the RSC's workshops have clearly excelled themselves. Some of the props and devices almost deserve applause in their own right.

It has to be acknowledged that the timing of some of the farce is not quite there yet. As the run develops – and there are months to go for this repertoire production – things should settle down and sharpen up, adding even more pace and punch to the humour. And as a counterpoint to the Shakespearean heft of the Rome season in the main house next door, there's an awful lot to be said for a bit of silliness in The Swan.

Vice Versa runs at The Swan Theatre, Stratford-upon-Avon, until 9 September 2017.