'One of yours?' I ask. He looks at me, pityingly. 'Still don't understand, do you? They're all mine 'ere, son.'
Mr Beackon is exaggerating, but perhaps not much. Six months ago this unemployed van driver from Limehouse became the BNP's first councillor. In May, his unashamedly racist party aims to take control of the Isle of Dogs neighbourhood council in London's East End - and the pounds 23m a year it spends.
Mr Beackon was elected for Millwall, part of the Isle of Dogs, by a majority of just seven votes, in a viciously fought by-election. Now, though, on a bright Saturday morning, with shoppers waving and smiling, it is hard not to believe him when he says that the BNP has seized the initative on Millwall's traditionally Labour council estates.
Mr Beackon canvasses and leaflets the estates with grim regularity, usually accompanied by as many as 40 of 50 young men, mainly 'islanders', in Identikit black leather bomber jackets and light blue, stonewashed jeans. Most have cropped hair.
Today there are also a handful of women in his team, and minders who have come down from head office. They include the BNP national organiser, Richard Edmonds, and the smooth spoken national press officer, Michael Newland, an unemployed accountant. They scent that the Isle of Dogs is within their grasp.
How is it that such traditional Labour territory has come so close to becoming a trophy of the extreme right? The saga begins in the Eighties with internecine squabbling in the local Labour Party. The party organisation was taken over by middle-class 'outsiders', some with Militant connections. They supposedly gave preference to 'Asians' classified as homeless or with large families, at the expense of 'sons and daughters' of current (white) tenants when allocating scarce council accommodation.
Last year, the old guard - working-class 'islanders' whose base lies in council tenants' associations - regained control of the local Labour Party on a populist ticket, but there was still no unity. Labour is forced to use activists from other areas to boost numbers on occasional, flag-showing exercises. This works to the advantage of the BNP. 'You get these ethnics and Anti-Nazi League people coming down here telling us islanders we are all racist bastards. It just pisses people off with Labour,' says a BNP canvasser.
The Liberal Democrats, who control the rest of the borough of Tower Hamlets, have never had a firm foothold on what locals call 'the island', and what support they did have is being leached away to the BNP. As for the Conservative Party, it is simply not a serious player here.
Following Derek Beackon's victory last year, the coming local election is a grudge match between Labour and the BNP - and so far the BNP is looking depressingly good. The island would be a considerable prize. This is largely because Liberal Democrat-controlled Tower Hamlets has, uniquely, devolved virtually all its power to seven neighbourhood councils, and the Isle of Dogs is one of these. Each neighbourhood council has its own budget and mini town hall, each hires and fires its own staff of thousands - and sets its own policies for housing, welfare and social services and other local authority activities.
At present, the Isle of Dogs council is run by Labour from Jack Dash House, a luxurious post-modernist centre leased to Tower Hamlets at a peppercorn rent by the London Docklands Development Corporation. It was named by Labour councillors after the Communist docker who lived in Millwall and whose constant wildcat strikes contributed to the destruction of the Port of London a generation ago - which says a lot about the sort of Labour Party Millwall boasted. Mr Beackon has pledged to change the name to Oswald Mosley House if the BNP comes to power.
The Isle of Dogs council is currently controlled by a mere five councillors, four of them Labour. All the BNP has to do on 5 May is to pick up two more seats and it will have taken control. Socialist policies will be replaced by those outlined in a leaflet that Mr Beackon was handing out on the estates. This pledges the BNP to 'defend the rights of White communities who have been forced to live in a multi-racial hell' and to 'put the British people first in jobs, housing and social welfare'.
AS WE cross the Barkantine precinct, I ask Mr Beackon how things have changed since his election. 'We used to see gangs of Asians hanging around. Now they stay indoors more,' he says. His heavies grin and mutter agreement. 'Now we've got a seat on the council, we're respectable. People who agree with us aren't afraid to say so.'
After Mr Beackon's election, the Labour majority on the neighbourhood council banned all political surgeries by councillors at Jack Dash House. It was a one of a number of moves designed to obstruct Mr Beackon. He claims it has backfired. 'They (the Labour councillors) done us a favour. They forced us to find people who would let us use their houses for surgeries. Now it's like visiting friends.'
And what was he telling people on these friendly visits? 'I don't tell them nothing much. They tell me. We all agree there are too many Asians. They shouldn't be here. It's time to start repatriation.'
Mr Beackon claims that he collected a 'a few black votes' last September and has 'no objection to your ordinary Black West Indians'. As we walk towards a row of shops, a BNP lookout on a mountain bike rides up and gives the lie to this claim. 'Two niggers with a bloody great dog round the corner,' he reports succinctly. The group tightens round Mr Beackon as we pass a couple of burly Rastas with an alsatian pulling on its lead.
After the procession has gone by, one of the Afro-Caribbeans, who would be identified only as Gary, is incredulous at the thought that any of his friends had voted BNP. 'I ain't scared of them, man, but I think they want to start a race war. If they touch me I won't call the police. We'll kill them.'
There had been some jeering at the black men from the BNP team, although Mr Beackon's head office minders suppressed it efficiently enough. Playing on what it regards as its home ground, the BNP wants its supporters to be on their best behaviour. They are out for the votes of what was once called the respectable working class rather than the lumpenproletariat. 'We've had a few people with swastikas and the like turn up, but we freeze them out,' Mr Newland assures me.
Mostly, the lads accept the injunction to behave, although there are lapses of taste. Some frightened little Asian girls are surrounded and leaflets thrust into their hands. 'Take them home to your Dad,' they are told before they are allowed to go on their way. Off they run, followed by guffaws and gibes from the men in black bomber jackets.
AFTER a couple of hours, I turn back and recanvass a dozen houses and flats at random and alone. I find two Asian families, neither prepared to talk. Whatever their politics, the white people complain bitterly about what they see as the influx of Asians on to their estates and into their primary schools. One young mother says she has converted to Roman Catholicism in order to get her youngsters into the only school that Muslims do not attend. Her friend has a convoluted tale about her child being asked by the school for money to buy prayer mats.
From nobody is there principled criticism of the BNP, although one young man does make a furtive fist, jerks it up and down and whisper 'wankers]' Another lad says he voted for Derek Beackon but would vote Labour this time because he thinks Labour has learnt its lesson and will no longer be giving preference to Asians.
When I rejoin the canvassers, John, a rather thoughtful computer specialist who has bought his own house on a new development, turns on me. 'You're not going to write a word about any of our policies, are you?' he says. 'You're just going to write about us being racists.' I reply that I have heard nothing but talk about race from BNP activists - and from ordinary islanders - all morning. He shakes his head in disgust and walks away.