Mr Waterson, the town's MP for 15 years, told the Herald in an exclusive interview he was innocent and had not assaulted anybody.
"I have done nothing wrong and did not assault anyone." said Mr Waterson, who is the Conservative party's shadow Minister for Work and Pensions.
The 57-year-old lawyer was arrested in the early hours of Monday morning after officers from the Metropolitan Police were called to his weekday home in Beckenham.
Mr Waterson called the police himself and it was while officers were at the house that the assault allegation was made.
He spent more than 13 hours in custody being questioned before being released without charge. He was released on police bail and is due to return to Bromley Police Station in March.
News of Mr Waterson's arrest is believed to have been leaked to a daily national newspaper reporter on Monday and the story hit the headlines in the following days.
Scotland Yard later issued a statement saying, "A man
was arrested at an address at around midnight on Sunday in connection with an alleged assault. Detectives from the Child Abuse Investigation Command are investigating. The allegations are not of a sexual nature."
On Wednesday Mr Waterson said he was unable to comment on the allegations made because of legal constraints but did say he and his wife, Barbara, had been inundated with messages of support and goodwill
The MP told the Herald, "Barbara and I would like to thank all the friends and colleagues who have contacted us with messages of support in recent days."
He added, "I called the police to an incident on Sunday. I have done nothing wrong and did not assault anybody. I have not been charged with anything.
"I am constrained in what I am able to say by law, but when this matter has been finally put to rest, we will be free to make a fuller statement."
Among the messages of support this week was a call from the chairman of the Conservative Association in Eastbourne, Millie Skriczka.
Mrs Skriczka said she had spoken with Mr Waterson after his arrest.
She told the Herald, "Nigel Waterson is an excellent constituency MP and the association is supporting him."
And at an officers' meeting of the association on Wednesday night, which had been planned for some time, members gave Mr Waterson a unanimous vote of confidence.
Mr Waterson, who divides his time between the house in Beckenham and his home in Wannock with his wife, Barbara and their two children, was first elected Member of Parliament for Eastbourne, Willingdon and East Dean in 1992 and at the last election in 2005 he held the Eastbourne seat with a majority of 1,124.
Mr Waterson spent the weekend before his arrest in Eastbourne on a range of engagements.
The MP, who has continued with his work in the House of Commons this week, said he would be returning to Eastbourne this weekend and it would be business as usual.