A man who blusters his way into high office while knowing nothing, a life turned upside down by a numerical fluke .... The theme of The Pirates of Penzance feel suddenly modern and familiar, but that is the gift of WS Gilbert, the librettist who ridiculed the powerful and the system.

Throughout Mike Leigh's pointed production for English National Opera, now boisterously returned to the Coliseum, I found myself wishing we had a WS Gilbert today, filling theatres with audiences who could laugh openly at the absurdities of their topsy-turvy nation, and others. Gilbert and Sullivan (a composer always at his best when tongue in cheek) may feel like whiskery old gents from this distance (Pirates was first staged in London in 1880), but in their day they were as radical as any mud-slinging stand-up now.

Their gift was to package their political satire in such delectable music, decorous dialogue and hilarious songs that nothing felt too dangerous. And a good production, like this one, of G&S lets librettist and composer do the work, and does not try too hard to embellish it.

So the pirate-ship scene that opens the show is performed on the first of a series of Alison Chitty's simple geometric sets – no rigging, no masts, just trunkfuls of rag-and-bone wear for the seamen and a steam-punk, glam-rock get-up for Ashley Riches' towering, airy, Pirate King. When a tide of single women rolls in, all candy stripes and cambric, button boots and boaters, the fate of everyone of marriageable age is sealed. Except Frederick, who on becoming 21 discovers that he was born on 29 February, and has therefore, so far, only just passed his fifth birthday.

His salvation is the plucky Mabel, here in the form of the prestigious Susan Chilcott prize-winner Soraya Mafi, who artfully steers a course between operatic coloratura and music-hall soubrette, in a very winning performance. Wide of eye and with a knowing command of her pearlescent voice, as piratical Frederick's first beloved she quickly is crowned Queen of the High Cs. Long may she reign.

As the ill-qualified, paternal, Major General, ENO's great comedian Andrew Shore rattles through his patter song, explaining that he knows, as someone else in high office might say, a bunch of stuff, but cheerfully admits to knowing nothing about the job he does. Remind you of anybody?

Opera veteran John Tomlinson's Police Sergeant delivers the lament for his lot with all the heft of his long career in grand opera, but with a lightness of touch, like Lucy Schaufer, as Frederick's old nurse, Ruth, while rising star David Webb is an amiable Frederick.

I've seen a life-time of amateur productions of Gilbert and Sullivan (I was playing in the pit for some, 45 years ago). Seeing this production for the first time, maybe it's the venue, and the expectations that come with walking into the Coliseum, home of English National Opera, or maybe it's the long operatic pedigree of this cast, but I have never been so moved by Sullivan's gift for pastiche – his Verdian choruses, the chorales and madrigals.

Yes, The Pirates of Penzance is a hoot and a scream, but there are moments of great beauty too – Gareth Jones conducting the ENO orchestra and chorus master James Henshaw make sure of that –and we can all do with some of that right now.