It is hard to overstate the achievements of Dizzee Rascal, although enough people have tried. Four years since he won the Mercury Music Prize with his debut album, Boy in Da Corner, he has become the most successful rap artist Britain has produced.

Shortlisted for the Mercury again this year for his third album, Maths + English, the 22-year-old Dylan Mills – as he is known to his mum – has taken his hardcore mix of garage, grime and hip-hop from the pirate radio fringes into the heartland of indie rock. Later this month he will be touring with Babyshambles and the View, and the crowd at the opening night of his tour in Glasgow was comprised overwhelmingly of college kids and NME readers out for a night of Hallowe’en fun. A hooded kid waved an axe over the heads at the front in time to the beats, and among the fancy dressers a fully clad Optimus Prime was chatting up Wonder Woman.

But Glasgow is a long way from the garage/grime stronghold of London and the South East, and to begin with, Rascal struggled to get the audience fully engaged. Accompanied by his shadow MC Scope and the appropriately named DJ Semtex, who produced a range of beats and rib-rattling bass notes that exploded from the PA like depth charges, Rascal powered through a bunch of tracks, new and old, with all the harsh, declamatory vigour he could muster. But the audience response to the age-old question of “What’s my name?”, during Jus a Rascal, was lukewarm at best.

The turning point came when Semtex broke off from his usual beats and instead played snippets from a string of rock favourites – I Bet you Look Good on the Dancefloor, Smells Like Teen Spirit, Seven Nation Army, I Predict a Riot. This was a popular but dangerous gambit. Was the star of the show going to rely on other people’s songs, or was his own material strong enough to carry the day?

But with the crowd suitably galvanised, Rascal moved swiftly and smoothly back to his own agenda with a pulverising version of Sirens and an equally insistent stomp through the Public Enemy-influenced Pussyole (Old Skool).

The hip-hop magic began to work at last, and from there Rascal powered his way with fresh confidence through the rattling drum’n’bass groove of Incredible, a mildly frantic song “for the ladies” called Flex, and a big, bouncing finale of Fix up, Look Sharp.

It was hard work at times, but he got there in the end.

Tour continues at Leeds University, Nov 2 2007; Oxford Academy, Nov 3; Bristol Academy, Tues Nov 6; Southampton University, Thur Nov 8; Astoria, London, Nov 9

Editor's choice

• The End: the worst movie endings ever
• Introducing The Times Proms Podcast
• Heath Ledger tipped for Oscar