Labour MP John Grogan's Early Day Motion is gathering cross-party support. He said: "It looks like being one of the best-supported and that puts pressure on the government to take some action."
Grogan said the off-trade should follow pubs and clubs with a code of conduct banning alcohol at knockdown prices.
He said: "Pubs and clubs have to sign up to a code that outlaws irresponsible price promotions. We don't often see
promotions saying 'come in and drink
as much as you like for £10' anymore,
so that's what we'd be looking for as
well as a ban on selling alcohol as a loss-leader."
The EDM will remain open until November. Grogan said: "I think a lot of the pubs and corner shops are writing to MPs to urge them to sign it, which is why it's going up so rapidly. Smaller shops can't really compete with supermarkets which sell 20 cans of Stella for £9."
The Competition Commission has recognised that supermarkets use alcohol as a loss leader, but Grogan said two pieces of evidence would prove they were not competing fairly. "One is that small shops who see alcohol as an important way to increase footfall can't compete on price. Also brewers and niche suppliers couldn't possibly discount to that extent."