Prime Minister Theresa May has refused to sack a top government adviser after he compared the UK's plan split from the EU to the British appeasement of Nazi leader Adolf Hitler in the 1930s.

But Downing Street reportedly stressed that May "completely disagrees" with Labour's Lord Andrew Adonis, who chairs the National Infrastructure Commission.

Adonis, who took the post in April and served as transport secretary under Labour Prime Minister Gordon Brown, made the controversial comments to The House Magazine.

"My language is usually pretty subdued in politics but anyone with a historical sense – and I'm a historian – recognises that leaving the economic institutions of the European Union, which have guided our destiny as a trading nation for half a century, is a very big step and the importance can't be over-emphasised," he said.

"To my mind, it's as big a step that we're taking as a country as decolonisation in the 1950s and 60s and appeasement in the 1930s. We got it right on decolonisation; we got it wrong on appeasement and I think we're in serious danger of getting it wrong in the way that we leave the EU."

The remarks were published just a day after the government tabled the Great Repeal Bill in parliament. The draft legislation is designed to scrap the European Communities Act and put all current EU law onto the UK statute book so that MPs and devolved administrations can repeal, amend or build on EU legislation after Brexit.

But the bill, which must pass through the House of Commons and Lords to become law, faces parliamentary "hell" as Labour and the Liberal Democrats fight Theresa May's so called "hard Brexit".

The plan could see the UK splitting from the EU's single market and customs union as well as stopping oversight from the European Court of Justice.

"This bill might keep a few restless people on the Tory backbenches from looking around for her replacement for a couple of months, but it has all the hallmarks of someone in office but not in power," said outgoing Liberal Democrat leader Tim Farron.

"I am keen to work across party lines with opposition parties of all shades to find common ground. These vital protections, enshrined in European law, from workers' rights to the environment, matter, and we will defend them to the hilt."