Two things are always said about the London borough of Tower Hamlets. One, that it's a place of extreme contrasts, from the historic East End to the shimmering banker megaliths of Canary Wharf, and two, that its politics are vicious. Both are true.

At the centre of all this stands Lutfur Rahman, the borough's first executive mayor and the country's most controversial local authority leader. Rahman attracts a lot of media attention; not least on Monday evening, when the BBC's Panorama programme will examine his record and those of other directly elected town hall chiefs.

The media attention Rahman attracts is rarely complimentary. A solicitor specialising in family law, Bangladesh-born but Tower Hamlets-raised, he describes himself as a liberal and a social democrat but others – in what may be political smears – have described him as secretive, sly, inept, a bully, anti-gay, the creature of hard leftists and a "frontman" for Islamists. He is as reviled by opponents as he is good at winning elections. The Labour party has learned this the hard way.

In 2010, Rahman, who had briefly led the council for Labour before the mayoral system was introduced, twice failed to make the party's panel-picked shortlist for mayoral candidates, but was added to it after taking legal action. He won the subsequent selection ballot of Tower Hamlets party members handsomely, only to be dumped by Labour's national executive committee.

He ended up fighting the borough's first mayoral contest as an independent, thrashing the fellow Bangladeshi installed to replace him into a distant second place, and beginning a four-year term that will come to an end when he seeks re-election in May.

The resounding endorsement of 2010 has not lessened unflattering interest in him. There have been recurring unproven accusations of dubious relationships with dodgy businessmen, voting improprieties, dirty campaign tactics, lack of transparency and the giving of grants to community organisations in the tacit expectation of en bloc ballot box support. These may simply be politically motivated slurs, but have added to the controversy.

Panorama's limited pre-publicity says it will investigate claims that Rahman has "used public funds both to promote himself and to create a political power base" and says that it has evidence "suggesting" the mayor has refused "to answer opposition questions about spending decisions involving millions of pounds of public money".

Throughout this onslaught, much of it tendentious, Rahman has denied any wrongdoing. And certainly some of the graver charges made against him have crumbled: asked to examine claims of undeclared campaign donations from a restaurateur, the police found no case to answer. A Labour investigation following allegations that Rahman won its mayoral candidature with the help of ineligible voters found no evidence of this.

One of the more spectacular stories about Rahman's administration appeared in 2012 when the London Evening Standard reported that the council was "threatening" to end a gay pub's drag queen-hosted amateur strip night using proposed new regulations for controlling lap-dancing clubs. The council has always denied this and says the measures, approved last September, will not affect the pub. By contrast, Rahman's welcoming the East London gay pride march to his borough in 2011 received little coverage. Rahman presents his first mayoral term as a defiant battle against central government cuts, citing his provision of education maintenance allowances for Tower Hamlets pupils after the coalition scrapped them, introducing free school meals for all primary-age children and overseeing a house-building delivery record recently quantified as bigger than Birmingham's.

A problem for Labour, which has Rahman on its hit list for May's local elections, is that he seems to draw strength from his enemies' assaults. A strategist on the party's disastrous 2010 campaign remarked on his aptitude for "political jujitsu" – echoes, perhaps, of George Galloway's bitter and sensational general election triumph in Bethnal Green and Bow in 2005.

Rahman's core support is substantially among his fellow Tower Hamlets Bangladeshis, who comprise around 30% of the borough's population. The council argues that grants for community projects represent a tiny part of its budget and that those to Bangladeshi schemes are rightly supporting some of the borough's most disadvantaged residents.Labour doesn't doubt that the mayor will get his vote out.

The party's challenger this time is John Biggs, another former leader of the council, who now represents Tower Hamlets and two other east London boroughs on the London Assembly. He offers a measured view of his opponent, acknowledging that many in the Bangladeshi community see Rahman as their wronged champion, fighting hardship and discrimination.

Biggs calls it "lazy" to say Rahman is "in league with fundamentalists", pointing out that Muslim activism isa legitimate part of the local political landscape and encompasses a wide spectrum of views, including within individual groups. His central case is that Rahman isn't up to the job of mayor, characterising him as inward-looking, weak and doing too little to help Tower Hamlets be the opposite.

But he also accuses the mayor of being "big on patronage", preoccupied with nurturing his bedrock backers and so risking sowing division in a culturally diverse borough. Unlike the first Tower Hamlets mayoral election, May's will be held on the same day as the vote for borough councillors. Biggs hopes this will increaseboth the turnout and his chances.

Meanwhile Eric Pickles, the local government secretary, said he would be "carefully examining the evidence" provided by Panorama". Whatever happens next in Tower Hamlets, it is going to be a tough and ugly fight.