In his statement Mr Burley said it had been a “huge privilege” to represent his constituents and that he would continue to work for them until the election. He made no reference to the controversy surrounding his departure.
The 35-year-old MP had repeatedly apologised for his actions, including in a letter to the JC after details of the party were made public.
But that letter appeared to come back to haunt him last month after it was revealed in a French court that he had arranged the hire of the SS costume — a point he had not made clear in his apologies — two years ago.
Mr Burley was sacked as a Parliamentary private secretary after the original incident.
On Tuesday, former Tory minister Sir Gerald Howarth had come to his defence, saying the episode had been a matter of “high jinx”.
The veteran MP called the reaction to Mr Burley’s involvement in the revelry “wholly out of proportion” and said people needed to “move on”.
He likened the incident to Prince Harry wearing a Nazi uniform and swastika armband at a party nine years ago.
Speaking on BBC radio in the West Midlands, Aldershot MP Sir Gerald said: “We all do silly things from time to time”, and accused the Mail on Sunday of leading a “witch-hunt” against his colleague.
He said: “I think it’s utterly disreputable. It’s wholly out of proportion. It’s been investigated internally by the Conservative Party and that’s the end to it.
“For Labour MPs to get involved is quite disgraceful. I mean Prince Harry dressed up in some sort of uniform. The former Archbishop of Canterbury dressed up in a German military uniform.”
Sir Gerald said Mr Burley was a “very worthy MP” for the Cannock Chase constituency and called on people to “get this in perspective”.
Mr Burley had been “picked on” because he “happened to have the guts to stand up to the Mail on Sunday”, said Sir Gerald.
“They’re going for him with all the power the media has. This is what they do to people. This is why the Leveson Inquiry was so important. Not to protect Members of Parliament — we can look after ourselves. But ordinary people get this treatment and they get no comeback.
“I don’t think the newspaper should decide these things. It’s not as though he has declared some sort of unacceptable policy. He has been engaged in some high jinx. We’ve all done it from time to time. Let’s move on, leave the guy alone.”
Earlier this week Mr Burley’s fiancée, local councillor Jodie Jones, said she had resigned as chairman of his Staffordshire constituency’s local Conservative association.
Ms Jones had been accused of a conflict of interests but claimed she quit the role before the association discussed Mr Burley’s future last month.
She also attacked the Mail on Sunday, claiming the newspaper was “hounding” her friends and family.
