Andy Burnham's triple whammy in Labour leader race

Andy Burnham's Bank Holiday weekend was spoiled by a trio of awkward stories: first, it was reported that he has been claiming expenses for the rent of a London flat when he already owns one nearby; then there was speculation that David Miliband might launch a bid for the Labour leadership before the next election; finally, it's reported today that the powerful Unite union might withhold support for his leadership bid.

One, the London flat. Since July 2012, Burnham has been claiming £1449.98 a month for the rent of a flat in Kennington – a favoured spot for MPs' digs because it's just over the bridge from Westminster – when he already owns a flat in the same area, The Sunday Times reported.

The amount he's claiming is just short of the maximum £1,550 allowed. The arrangement is entirely within the rules, the paper said, but Sir Alistair Graham, former chairman of the committee on standards in public life, said it showed "a lack of judgment".

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Burnham has issued a "full explanation" on his website telling how a change in Commons rules gave him "no choice" but to quit his flat and rent it out.

Two, the David Miliband story. Senior Labour figures are "plotting" for Ed Miliband's brother to return to England from New York to play a major role in the Stay In Europe referendum campaign and use it as a springboard for a leadership bid in 2018, The Sun reports.

In short, Burnham, still the bookies' favourite among the current candidates, might be elected Labour leader this autumn but would face pressure to have David Miliband replace him in time for the 2020 general election.

The Sun reports that the veteran Labour MP for Huddersfield, Barry Sheerman, might be happy to stand down in 2018, creating a by-election that would give David an easy ride back to Westminster politics. The fact that Sheerman's daughter works for David has added fuel to the speculation.

Three, the Unite threat. Senior figures in Unite are angered by Burnham's secretary's failure to adopt an "anti-austerity" economic policy, the Daily Telegraph reports.

The union has been signing up around 1,000 affiliate Labour members a day through cold-calling and "getting shop stewards to encourage individual union members to join on the spot".

It had been assumed that Unite's general secretary Len McCluskey would then urge them to back Burnham. Not any more, says the Telegraph, which quotes a "senior Unite source" saying: "Instead of having a right-wing economic policy we want a progressive left-wing policy. It doesn't look like Andy Burnham has shone there…

"No matter what is being said in the parliamentary village, out in the trade unions and the Parliamentary Labour Party … there is no demand for a switch back to the Right or back to New Labour."