I cannot claim to have been to Redwell in Wellingborough, Northamptonshire, although on paper it would seem a pretty pleasant place, rather more prosperous than average. I have been through Yapton, in Arun, West Sussex, and that is distinctly desirable territory. I think I have cut across Lawford and New Bilton, in Warwickshire, too and while it was not quite the Cotswolds it was hardly a centre of deprivation or tense race relations either.

All of which makes a recent pattern in local council by-elections more unexpected. A by-election was held in Redwell West last Thursday. The Conservatives easily retained the seat but there in second place, eight votes ahead of Labour and with four times the strength of the Liberal Democrats was the British National Party candidate. At Yapton, seven days beforehand, the BNP had come third, a mere seven votes behind the Liberal Democrats, and with almost a fifth of the vote. A fortnight earlier Lawford and New Bilton had witnessed a cracking contest with Labour hanging on by a single vote over the Tories and with the BNP securely third on 15 per cent, well ahead of Nick Clegg's contender.

It is being said that the local elections on May 1 are a rather boring affair with the obvious exception of the battle between Ken Livingstone and Boris Johnson to be the mayor of London. The BNP, however, will be more interested in the Greater London Assembly than whether Red Ken or the Blue Blond wins control of the capital city. For the complex electoral method - the additional member system - used for the assembly means that any political party has a decent chance of winning one of the 25 seats at stake if it can accumulate 6 per cent or so of the vote in the party list section of the ballot paper.

This is far from an impossible target for the BNP. The last local by-election conducted in London was on March 20 at Gooshays in the Borough of Havering. The BNP had narrowly won it in May 2006 in something close to a statistical fluke but now had to defend it after the departure of its councillor. It was assumed that this might be a challenge for the BNP. Far from it. Its share of the vote went up from 28 per cent to 38 per cent. The Liberal Democrats, for the record, managed the singularly strange feat of finishing sixth.

The ward of Gooshays is striking for the lack of immigrants who live there. The ward is 96.4 per cent white, making it one of the least ethnically diverse in London. The place, however, is polarised by age (disproportionately large numbers of very young and very old voters), has comparatively high unemployment and very low levels of educational attainment. It is ideal terrain for the BNP and there are other Gooshays in London. That being so, the stealth success of the BNP could be the real story of the local elections.

This is surprising in many ways. Not least because the BNP has been through a period of fratricidal factionalism. There have been purges, resignations and attempts to establish rival nationalist parties. Some within its ranks have accused the leader, Nick Griffin, of “dictatorial tendencies” (fancy joining a neo-fascist party and then discovering that the führerprinzip reigns there) while others consider him a bit of a pinko for wanting to play down race in an effort to become more respectable.

None of this internal anguish appears to matter much at polling stations. Stick a BNP champion up in a local by-election and he will accomplish 10-20 per cent in swaths of England. On that evidence, the BNP will have its triumph in London.

So why do I expect the BNP to do well? There seem to me to be three factors that might prove important.

The first relates specifically to the forthcoming local elections. The last time that this set of seats were fought was in June 2004 when the tussle in London and councils elsewhere were combined with elections for the European Parliament vote in an attempt to raise the turnout. It did, but it was the UK Independence Party that benefited from these joint elections, not only doing very well in the battle for the European Parliament but in the locals too - it seized two Greater London Assembly seats, for example. The typical UKIP and BNP supporters are by no means identical but there is a degree of overlap between them and the surge for the former did diminish the prospects of the latter. On May 1 there will be no European Parliament poll to help UKIP - which too has suffered from schisms of late - by pushing Europe towards the top of the agenda.

The second factor is that the BNP has improved its organisation. The in-house feuding has not prevented the BNP from honing a much more sophisticated approach to campaigning. The quality of its leaflets has improved, there have been instances of it engaging in telephone canvassing and reports of more “mystery shopping” where its activists blitz an area to market test the public reaction to the party and then determine whether it is worth fielding a candidate.

The final dimension is the most significant. The optimal conditions for the BNP are where there are substantial numbers of disillusioned ex-Labour supporters and a Conservative Party that is wary of concentrating on subjects such as asylum-seekers because it wants to appeal to mainstream metropolitan opinion. It is also a bonus for the BNP if the Liberal Democrats look more centrist and are not indulging in populism to chase the protest vote. These are precisely the political circumstances that will be at play in the local elections of 2008, especially in London.

The main constraint on the BNP in London is how well it can stretch its limited resources. It won 4.8 per cent of the assembly vote in 2004 even with UKIP in the frame. If it can win anything close to double that this time, then regardless of whether it is Mayor Ken or Mayor Boris, it will be the BNP that provides the shock of this election.

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