The British National Party is on course to win its first seats in the European Parliament this year, Gordon Brown has been warned. Senior Labour figures have told the Prime Minister they believe two BNP candidates are likely to be sent to Brussels under the proportional representation system of voting, The Independent has learnt.

They fear Labour’s campaign for the European election in June has been too slow to get off the ground and its lack of preparation is allowing the BNP to win over disaffected Labour voters.

Yesterday, the far-right party was celebrating a surprise win in a council by-election in Swanley, Kent, where the BNP candidate took 41 per cent of the vote after Labour’s support collapsed.

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It is the first time the BNP has won an election in a southern English county, and shows it is broadening its appeal beyond its traditional northern heartlands. The party also polled more than 28 per cent of the vote this week in a council by-election in Thringstone, Leicestershire – a seat it had never contested before.

Mr Brown has been told the BNP has a strong chance of fielding successful candidates in the North-west of England and Yorkshire and the Humber. A senior Labour source told The Independent yesterday: “We have got to get our act together – and very quickly. No one is focusing on the European elections; no one knows who is in charge.”

Last night, the former minister Peter Hain warned that every political party was guilty of “complacency” over the threat posed by the BNP.

He said: “Everybody across the political spectrum – especially the Labour Party – has to prioritise beating the BNP with a vigorous strategy based on grassroots politics to win local trust and also making sure we deliver on affordable housing and deliver on jobs.

“There is very fertile territory for [the BNP] now. When people are losing their jobs and there is an economic downturn... it’s heaven-made for them.”

Labour officials believe the BNP is well placed to attract support from the UK Independence Party, which won 16 per cent of the vote at the last European election, but has since imploded. They are also worried that disillusionment with the Government among traditional Labour voters will tempt them to support the BNP or not turn out at all.

The UK is divided into 12 regions for the European ballot, with voters asked to back parties rather than candidates. In practice, a party must win between 8 and 13 per cent of the total votes cast to have at least one representative picked from a list of nominees, depending on the size of the region.

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In the North-west, where the BNP leader, Nick Griffin, is its main candidate, the party has to add only two or three percentage points to the 6.4 per cent of the vote it secured in 2004. In Yorkshire and Humber, where the BNP polled 8 per cent last time, it probably has to increase its support by three or four points.

Jon Cruddas, the Labour MP for Dagenham, who campaigns against the far-right group, acknowledged that conditions look better for the BNP now than they did five years ago, when it last came close to winning a seat.

Mr Cruddas said: “Five years ago, Ukip did very well and five years ago we had a benign economic environment. Now there is a global crisis. Everything else being equal, it’s going to be tricky.”

The BNP’s ability to spring surprises in previous no-go areas was underlined on Thursday during the ballot in Swanley St Mary’s, which used to be a rare, Labour-leaning ward on the Tory-controlled Sevenoaks District Council. The BNP’s Paul Golding captured it with a majority of 76 over Labour. The Tories finished third.

Mr Golding said afterwards: “I’m going to put British people first on the housing queue. I’ve had lots of complaints that foreigners and asylum-seekers are getting ahead of them.”

A Labour activist, Lesley Dyball, claimed that a group of people who walked out of the building where the polling station was sited, holding what she believed to be a BNP leaflet, were laughing and shouting “blacks out”.

The BNP’s victory at Swanley follows its near-miss last month in an election in the neighbouring London Borough of Bexley. Simon Darby, the deputy party leader, said it would mount a vigorous contest in the European elections, adding: “We are in place for 10 seats and we’ve worked out if we can secure around 8 per cent of the vote we will take one of them.”

The BNP threat will be highlighted today at a London rally organised by the group Unite Against Fascism (UAF). Speakers include Mr Hain, the former London mayor Ken Livingstone and Ennio Odino, a Holocaust survivor. The UAF secretary, Weyman Bennett, said: “Hitler used the economic crisis of the 1930s to gain a hearing for racists and murderous policies.”