Newmark was was caught sending explicit images to an undercover journalist who posed as woman on twitter.
The 56-year-old married father of five offered his resignation after being informed that a national newspaper was about to publish full details of the exchanges.
In a letter to the Prime Minister, the MP for Braintree said he would quit at next May and stated:
The continued media intrusion into past episodes in my personal life is placing an intolerable burden on my family. I have therefore decided to stand down at the general election. I will continue to serve my constituents to the best of my abilities until that time.
I again appeal to the media to respect my family's privacy and to give me a chance to try to heal the hurt I have caused them.
I have no one to blame but myself and take full responsibility for my own actions.
I will remain a loyal supporter of the Government and would like to thank the many friends and colleagues for the support and sympathy they have shown me and my family.
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