Global pressure will force Australia to do more on climate change, Britain’s prime minister, David Cameron, has predicted.

Cameron told a committee of British MPs in London he sensed the Australian government recognised it did not want to be the international “back marker” on the issue.

“Look, it’s a sovereign country. It has to make its own decisions. There has obviously been a very big debate in Australia about carbon taxes and prices and all the rest of it,” Cameron said as he gave evidence to a House of Commons committee.

“But my sense is that they recognise they don’t want to be the back marker – nor should they. It’s a great country. It’s clearly affected by climate change and I believe they will do more.”

A Liberal Democrat MP, Malcolm Bruce, responded by telling the prime minister the US used to be the “back marker” on climate change policy, but “the truth is that Australia is the back marker at the moment”.

Cameron replied: “I don’t think they will want to be and I think they will feel pressure and want to do more.”

“We should try to encourage them to do it in their own way rather than say there is some pre-ordained route they have to follow.”

He said the US had managed to cut its carbon emissions thanks to the “unexpected bonus” of the “shale revolution” – widely known as fracking – which meant it was burning less coal.

“That’s enabled [Barack Obama] to, I think, make some quite interesting commitments on climate change which is being delivered through all sorts of executive motions rather than Congress,” Cameron said.

Bruce earlier quoted a European Union official who described the G20 climate discussions in Brisbane last month as “trench warfare”.

Cameron had joined calls at the G20 for Tony Abbott to do more on climate change, saying “countries that have so far done the least have to think about what more they can do”.

Obama had dramatically forced climate onto the summit agenda – against the wishes of Australia – with a hard-hitting speech urging the world to rally behind a new global agreement, pledging $3bn to the Green Climate Fund and pointing out that countries such as Australia had the most to lose from global warming.