As job applications go, calling your potential boss a “stupid, sanctimonious dwarf” is probably not the best approach to getting appointed.

But then, luckily for the former Transport minister Simon Burns, it is not up to House of Commons Speaker John Bercow to decide whether his critic should be given the role of his deputy.

Mr Burns, who stood down from his ministerial position, is the front-runner to be elected to the job which will be decided by a free vote of MPs in the next two weeks.

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He will be running against Nadine Dorries, the rebellious Tory MP who took part in I’m a Celebrity, Get Me Out of Here, as well as Eleanor Laing, the Conservative MP for Epping Forest, and Brian Binley, a long-standing right-wing critic of the Coalition.

Mr Burns is believed to have the support of David Cameron, who himself is no fan of Mr Bercow, as well as a lot of Conservative MPs.

Downing Street did not move to fill Mr Burns’ vacant ministerial position last night – suggesting there will be a wider reshuffle of ministers at the start of next week.

The vacancy arose after Nigel Evans, the former Deputy Speaker, resigned from the role after being charged with sex offences against seven men. Mr Evans, who was told in court yesterday that he will be tried on 10 March next year, was previously a Tory MP and by convention the job is expected to go to another Conservative.

Mr Burns has made no secret of his loathing for Mr Bercow and was one of the few MPs to refuse to shake his hand when he took the oath in 2009. In June 2010 Mr Burns was rebuked by the Speaker after turning to answer a question from a Liberal Democrat MP. With several Labour MPs shouting that they could not hear, Mr Bercow said: “I have just had members complaining that they can’t hear. You must face the House – it’s a very simple point.”

Mr Burns responded by mouthing the words “stupid, sanctimonious dwarf” to Mr Bercow, who is 5ft 6ins.

He was forced to make an apology, but later was to said have retorted, on being told the Speaker was not happy, “Well which one is he then?” – a reference to Snow White and the Seven Dwarfs.

Mr Burns’ decision to run as Deputy Speaker was welcomed by David Cameron, with the Prime Minister saying he was “hugely grateful” for his service. However, one Conservative backbencher said yesterday: “Burns has a lot of enemies from his dark days in the whips’ office. He is also at constant war with John Bercow and relations between the Speaker and his deputies needs to be professional and workmanlike – not petty and schoolroom like. Burns would make the speakers’ offices into more of a soap opera than they already are.”

Mr Burns said last night that his past comments would not affect his working relationship with the Speaker. “I am very professional when it comes to my work,” he said. “And I would be able to behave in a professional manner working with John Bercow.”