Gilberto Gil, Barbican, London

He strolls out to a roar of applause with an indisputable sense of cool, sporting a crisp white shirt, charcoal black trousers, and ash-coloured dreads. He takes his seat on a raised, centre-stage platform flanked by a couple of monitors, takes a minute or so to tune up as cameras flash all over the auditorium, and then embarks on a 20-song journey through four decades of music. It sounds simple, but it's pretty magical.

Gilberto Gil must have built up a few air miles in his regular concert visits to the UK over the years – indeed, he talks of London as his third home city, after Bahia and Rio. The links go back a long way. He was exiled here with Caeteno Veloso in 1969, after being arrested and imprisoned by Brazil's military government. Having already worked with Gal Costa, Tom Ze and the São Paulo psychedelic band Os Mutantes prior to incarceration, in London he settled first in Chelsea, where he developed a lifelong habit for the local football team (while introducing the samba "Chiclete" he stops to recall the team's late centre-forward Peter Osgood).

Gil later moved to Notting Hill, home at the time to the squats and dives of the "alternative society", where he fell in with the likes of the Incredible String Band, the Beatle George Harrison, and even with the scene's most far-out denizens, such as Nik Turner, sax player from acid reprobates Hawkwind. It must have been a strange brew of influences he took back with him when he returned to his original home city of Bahia in 1972.

By the end of the Seventies, he'd spent a lot of time in West Africa, and via hooking up with Jimmy Cliff and recording "No Woman, No Cry" in 1980, brought reggae music to Brazil – tonight's solo, acoustic readings of "Three Little Birds" and a Portuguese-language "No Woman, No Cry" are spine-tingling.

You can feel the heat of all these influences in his music. With Brazil's own vast stock of musical rhythms and forms to play with, as well as the dynamics of British rock, American blues and soul, and Jamaican reggae, Gil's music has melded together many different sources over the decades, and through tonight's one-man-and-his-guitar concert – augmented after half a dozen songs by Gil's son Ben on percussion and second guitar – you can hear snatches of rock dynamics or a bluesy roll blooming through the undergrowth of bossa, baiao and samba rhythms.

The opening "Maquina de Ritmo" is lovely, the weight of the guitar accompaniment bending to the song's vocal dynamics, and the following "Esoterico" rides on a poppier, rhythm and blues-inflected guitar line. As a performer Gil invites an intimacy with his audience, however large the arena, shrinking the scale of the Barbican Hall's concert platform to the intimacy of a front porch session.

He introduces "Metefora" as a song about "the special realm of the artist – the mixture of being in isolation and being so inside life at the same time", while a new composition, "A Faca e o Queijo" ("The Knife and the Cheese") is for his wife. "It's an inside-the-marriage song. When we met, I wrote her songs, and years later she complains that I haven't written her any more, so I wrote 'The Knife and the Cheese'. I hope she's pleased..."

It's one of a handful of strong, instantly catchy new numbers – his return to writing, he says, after four years – that augur well for a new album to be released this June. "There are tracks to be done when I get back home," he adds, "though it's a difficult time to dedicate exclusively to music. Speaking as a minister..." The pronouncement provokes a lot of laughter. There aren't many politicians you'd trust with an expenses form in this world, let alone with a microphone and guitar; in fact, Gil is probably the only one.