Fowler and Widdecombe were debating the former politician's proposals for a naming and shaming policy for anyone who gets "drunk and incapable" on a night out.
Widdecombe, who has recorded a documentary on the subject for Radio 5 Live, said: "I'm not talking about people who get merry or people who accidentally get a bit drunk. I'm talking about people who go out deliberately to get drunk. It puts a strain on the rest of us.
"The NHS can't cope and the police can't cope. I'm talking about serious excess."
Fowler was critical of Widdecombe's proposal, claiming that more responsibility should be placed on "pubs and clubs".
"I've worked in many bars and venues like that. When we were serving drinks, I'm sure it's against the law to serve a treble, so I was often encouraged to serve a double and then another shot on the side. That's not responsible to me," she said.
Fowler added: "If I go out and have a few too many and it ends up the paper or online, maybe I've got a warped sense of humour, but I find it funny.
"I got arrested about four years ago. It wasn't one of my most drunken nights. A lad came up behind me, grabbed my bum and I turned around and pushed him. It just happened that a policeman was coming around the corner when I pushed him. Would it be fair if I was shamed for that?
"What if someone had their drink spiked?"
At the end of the debate, she told Widdecombe: "I think what you should do is come on a night out with me and I'll show you how it works."
A defiant Widdecombe replied: "No. No thanks. No, ta. Thank you for the invite, but no."
Drunk Again: Ann Widdecombe Investigates is on BBC Radio 5 Live at 10pm on Monday, April 23.