By Brian Wheeler
BBC News political reporter
The British National Party has more than doubled its number of council seats in England from 20 to 44.
The BNP is led by Nick Griffin
But, historically, gains by far-right parties in UK elections have tended to be short-lived.
Oswald Mosley's New Party, formed in 1931, panicked the political mainstream when its candidates gained 16% of the vote, but it never came close to winning a seat at Westminster and was later subsumed into the British Union of Fascists.
In the 1970s, the National Front saw its popularity increase on the back of concern about immigration and working class voters' growing disenchantment with Labour.
In 1973, the party gained 16% of the vote in a West Bromwich by-election, but it averaged just 3% nationally at the next general election, where it fielded 54 candidates.
In the 1977 Greater London Council elections the National Front fielded 91 candidates - and the smaller National Party 22 - gaining a combined total of more than 100,000 votes.
In 10 constituencies the far right vote was above 10% of the total cast. In the two seats of Bethnal Green & Bow and Hackney South & Shoreditch it was 19%.
1997 General election:
2001 General election:
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2005 General election:
But by the 1981 GLC elections, the extreme right vote had slumped to 30,006, with just 462 votes per candidate, compared with 1,127 in 1977.
Since breaking away from the National Front in the early 1980s, the BNP has had sporadic success in local elections, particularly in its East London heartlands and, more recently, West Yorkshire.
The party's Derek Beacon won a 1993 by-election in the Millwall ward of Tower Hamlets but in the full borough elections the following May Labour won it back - on an extraordinarily high turnout, for a local election, of 66.5%.
Before Thursday's poll, the party had just 20 local councillors out of Britain's 22,000 council seats, all gained since 2002.
And although it fielded a record 363 candidates this time, it is still a long way from being able to put up a full slate of candidates across the country - either in local or general elections.
Nevertheless, there is growing concern among mainstream parties, who accuse the BNP of peddling hate and division, that it is learning to hold on to its gains.
It has steadily improved its performance in general elections, although its share of the vote in the 2005 poll was still minuscule, at 0.7%.
A handful of constituencies bucked this trend, with the BNP gaining 17% of the vote in Barking, beating the Liberal Democrats into fourth place. It gained 9.2% of the vote in Keighley, where chairman Nick Griffin was standing, and 13.1% in Dewsbury.
The party picked up nearly 200,000 votes in the 120 constituencies it contested and retained its deposit in 40 of the seats.
But the BNP's high water mark, before Thursday, came in 2004 when it was able to capitalise on racial tension in Blackburn and Burnley.
It gained more than 800,000 votes in that year's European elections - 4.9% of the vote, although it missed out on a seat in the Brussels parliament.
One opinion poll taken before this week's local elections suggested nearly one in four UK electors have seriously considered backing the BNP.
But there are also signs its support at the ballot box remains fragile.
It won 14% of the vote across Oldham's two parliamentary seats in the 2001 general election but fell back to just 6% in 2005.
Earlier this year in Keighley, it lost a seat on Bradford council, when Labour won by 503 votes.
Only time will tell whether the seats gained on Thursday are a sign of things to come or another flash in the pan.