It was supposed to be a quick trip to relaunch the career of one of the most successful hip-hop bands in Africa. Daara J, from Senegal, have headlined at Womad, won a BBC World Music award and performed alongside Wyclef Jean. Now a duo, renamed Daara J Family, and with a new album to promote, they were scheduled to play at the Jazz Cafe in London on Tuesday night before appearing on Radio 4's Midweek the following morning.

Instead, N'Dongo D and Faada Freddy found themselves in Paris, unable to board the Eurostar to London, because they had been refused entry to the UK by the UK Border Agency. They had visas to enter Europe, but not to cross the Channel. It wasn't through want of effort: their attempt to get to the UK had involved a trip from their home town of Dakar to Banjul in the Gambia, where they waited for three days at the British High Commission before being refused a visa.

Faada Freddy is confused and upset. "In Senegal, we were told there was no one to see us," he says, "so we had to travel to the Gambia to get our UK visas. There we were told that the people who were organising our London concert were supposed to have £800 in their account for us. So I asked them if they could ring the Jazz Cafe to check, but they refused. It's crazy."

Back in the UK, their record company is furious. "They are making it as hard as they can for black Africans," complains Ian Ashbridge of Wrasse Records. "And now Daara J's UK career is in tatters, and their album launch here is in the toilet."

He's not alone in complaining about the problems foreign musicians have in getting visas. Jah Wobble says he hasn't performed live for nearly two years because he is so furious at the treatment of the Chinese artists in his Chinese Dub project, one of the highlights of the 2008 Womad festival. "I wanted to bring them back in for more shows," he says, "but the British consulate in China turned them down. They thought they were going to stay in the UK, even though some have careers in Chinese opera." Nick Page of the Ethiopian fusion band Dub Colossus warns that "the world music scene will soon consist entirely of EU passport-holding musicians."

Over the past year, there has been a reform in the way that the Home Office issues visas to musicians. Like other foreign workers, musicians now need a "sponsor", often an agent or a concert promoter, who has been vetted by the Home Office and is charged £400 for a sponsor licence. The sponsors check on musicians while they are here, pay their expenses in the UK if they encounter problems, and are given sponsorship certificates to pass on to the musicians they want to bring in. According to one sponsor, David Flowers, an agent who looks after Tinariwen and the Buena Vista Social Club: "It's an instant system, no questions are asked, and in effect it replaces work permits."

The sponsorship certificate, though, is only the first step to getting a visa. Under the new points-based system for issuing visas, musicians must get 40 points. The sponsorship certificate wins them 30 points, and they get the final 10 if they can show that their sponsors will cover "maintenance requirements" in the UK. That is where Daara J came unstuck. Looking through their "refusal of entry" papers from Banjul, it's clear that they were awarded 30 points for sponsorship, but nothing for maintenance (hence that demand that £800 be available). So had a box been left unticked on the form?

For its part, the Home Office says: "Musicians' applications often fail because they haven't supplied enough evidence with the application form, and often they leave it too late before applying."

The system has its critics – not least because of its complexity. Nevertheless, some of the main sponsors responsible for bringing artists into the UK say there are benefits to this points system. David Jones, of the promotion and production group Serious, who is a member of the Home Office task force looking at visa problems, says: "It's now easier 50% of the time, though there are still problems."

The biggest of those problems is the UK's move to biometric passports. Once, musicians could send their agents across borders to get visas, but now they have to apply in person, every time they ask for a visa, so they can be photographed and fingerprinted. But in west Africa alone, there are no facilities to issue such visas in Mali, and the service in Senegal is slow, so applicants are advised to go to the Gambia, which is now the regional biometric processing centre (that is why Daara J were sent there). One popular alternative for those performing in Europe is to get a "Schengen" visa that covers the continent (but not the UK), and then apply for a UK visa in Paris – but again that can be a time-consuming and costly process, and it means musicians have to book their UK gigs and then hope they can get a visa when they reach Europe.

But does all this really matter to British music fans? Yes. The situation may have improved, but it's clearly still not fully understood by many musicians or their sponsors – in the case of Daara J, someone seems not to have realised that by not ticking the maintenance box, they were wrecking the band's chance of getting a visa. And now many African musicians have to travel to other countries to get visas, and then spend money waiting around in foreign cities, there's a danger that some will simply not bother to come here. Why go through the hassle and expense of getting a UK visa when it's easier to get a Schengen visa and play across mainland Europe? There are signs that is happening already. David Flowers points out: "Malian stars like the Rail Band now refuse to play in the UK because it's so complicated".

And despite the enthusiasm of some sponsors, there are concerns that the expense and bureaucracy involved might deter others. "Without maverick small operators, audiences will no longer get the chance to discover exciting unknown groups from the non-EU world," argues Page. Ashbridge agrees. "Would major African stars be here now if this system existed in the past?"

And as for Jah Wobble? "I had to do Chinese Dub myself," he says, "because no one else would touch it with a bargepole. This new system hits the small operator. I didn't become a bass player to be an unpaid civil servant."