Conservative MPs have piled pressure on Downing Street to consider hardline legislation on strikes after the Southern rail industrial action.

Theresa May and the transport secretary, Chris Grayling, held an emergency meeting at Downing Street on Monday night with 25 Conservative MPs whose constituencies are affected by the continued disruption.

At the meeting, the MPs backed the idea of extra commuter buses. Whitehall sources said the meeting was not a brainstorming session but instead an opportunity for May to listen to concerns.

The Guardian understands that the government believes a full bus replacement would be logistically impossible because of the number of vehicles required and the traffic at peak times. Trains run from some stations to London 10 times an hour, carrying 1,000 passengers each, underlining the complexity of any replacement bus service.

A source in the meeting said the majority of those present urged the prime minister to consider a more hardline stance on strike action, including new legislation to require that critical public services run at least 50% capacity on strike days and that strikes are “reasonable and proportionate”, which courts could adjudicate.

“Almost everyone there was expressing support for those ideas, because thousands of people can’t get to work,” the source said. “There is growing support in the wider parliamentary party too.”

Industrial action by Southern rail conductors in the RMT union and a ban on overtime by drivers in the Aslef union caused further disruption for up to 300,000 passengers on Monday and Tuesday.

More strikes are scheduled from 9-14 January, and Conservative MPs from London, Surrey and Sussex are eager to get new measures agreed before the new year. Southern has already advised commuters not to attempt to travel during the January strikes.

Chris Philp, the Tory MP for Croydon South, said the government needed to consider all options to help people get to work. “If the buses can help, it’s a good idea,” he said. “Anything that eases the problem even a little bit is worth doing.”

Philp, who authored a series of proposals on strike legislation including the proportionality test, said: “The unions talk about people’s right to strike but nobody is trying to remove it. The suggestions are about balancing the right to strike with the rights of the public to get to work and see their loved ones. Some constituents have been fired or had to quit their jobs because of this. What about their right to work?”

Henry Smith, the Conservative MP for Crawley, said those at the meeting had expressed concern not only about the strikes but about the performance of Govia Thameslink Railway, which runs Southern. “A number of things were discussed, a whole range of ways to improve services and end the strike action,” he said.

“Everything needs to be in the mix. It’s causing misery on a daily basis to passengers’ lives. People are losing their jobs, time with loved ones in the evening. It’s hugely damaging to the economy, so all ideas that are potentially viable need to be explored.”

On Monday the shadow transport secretary, Andy McDonald, said the government had the power to end the dispute. “We need to take the heat out of the current situation,” he said. “It’s vital that the parties agree to take a breath and there be a moratorium to enable some sensible, objective discussions to take place.

“As Southern commuters are well aware, services are delayed, cancelled and overcrowded every day regardless of strike action. For the sake of passengers, the government must take this opportunity to resolve the dispute and sort out Southern’s unacceptable service.”