A UKIP parliamentary candidate called a Merton councillor a "village idiot" for retweeting pictures of the anti-Conservative protest in central London on Saturday.
He claimed she was endorsing the defacement of a WWII women’s war memorial by a protester, which occurred after she started sharing tweets about the protest.
He wrote on Twitter: "Village idiot @maximartin02 re tweeting praise for violent protests that have seen war memorial desecrated. Absolute disgrace."
Mr Hilton's tweet calling her a "village idiot" was retweeted 15 times and favourited seven times. Coun Martin, said yesterday she was "still quite tearful he would suggest that I was supporting it [the memorial defacement]".
She did not re-tweet any tweets about the defacement of The Monument to the Women of World War II in Whitehall on Saturday.
But she re-tweeted three pictures with comments that the protest was taking place and claiming that it was not being covered by 'mainstream media' - before she said she was aware the monument had been vandalised.
She said: "Of course I would not support anybody defacing a national memorial to women and it's absolutely disgraceful and anybody who knows me would know how deeply I feel about past forces and I wouldn't support that."
She said she was watching TV with her family when she saw reports of the protest on Twitter and wondered why it was not being reported more widely.
Coun Martin, who is cabinet member for children's services, said: "My family is devastated...I have had comments coming back from people saying nasty things about me from as far as Canada, the North and the Midlands."
"He's a man who the night before when I entered the count at the election he walked over to me and told me I was looking lovely and the day after he's calling me the village idiot."
Mr Hilton said: "She was re-tweeting messages supporting these London protests just at the point where they were reaching their end and the women’s memorial had been vandalised."
He added: "Even if I accept what she says they she didn't know [about the vandalism] at the time, she didn't do anything to condemn the violence or call for calm and she didn't even reply [to my tweet]."
Coun Martin said: "I never reply to his tweets. He's always asking me things on Twitter but it's not the forum for intelligent debate."