The senior Lib Dem said Gauke backed leaving the EU with a deal, despite his conversion to a second referendum, making his politics incompatible with a party that wants to revoke Brexit.
Appearing on HuffPost UK’s Commons People podcast, Umunna also:
Revealed he felt he was not “ready” to become Labour leader when he pulled out of the race in 2015.
Said David Lammy would make a good Labour leader as he has “found his voice” campaigning for Grenfell victims and for a second EU referendum.
Suggested the Lib Dems could bring about a second referendum after the election without backing either Jeremy Corbyn or Boris Johnson as prime minister.
He spoke as the Lib Dems were forced to replace candidates who wanted to make way for Labour rivals in two seats to ensure a pro-Remain MP was elected instead of a Tory.
Umunna dismissed “patronising” and “unreasonable” demands for the Lib Dems to make way for Labour without Jeremy Corbyn’s party reciprocating.
And he explained that the party could not back Gauke, despite his conversion to a second referendum, because it would open the Lib Dems up to Labour attacks.
Umunna described the former work and pensions secretary as “the best of One Nation Toryism”, but added: “There are other people in the Liberal Democrat family who have other views on this.
“Remember, David oversaw over £12bn of welfare cuts coming through in 2015.
“I’m not surprised if you hear Labour people saying ‘why don’t you just adopt David Gauke as your candidate’ because then they can just attack us for basically having somebody who is an architect of £12bn of cuts.”
He also insisted Gauke’s case was different to the likes of former Tories Sam Gyimah and Phillip Lee who have joined the Lib Dems because they did not serve in the cabinet.
Umunna also dismissed questions about Lib Dem leader Jo Swinson’s decision to rule out a coalition or confidence-and-supply deal with Labour if there is a hung parliament after an election.
He suggested that if the Lib Dems win 50 to 60 seats, the party could bring about a second referendum without supporting anyone as PM as Brexit has created a new precedent in parliament which allows backbenchers to pass their own legislation.
“The issue of whether and who forms the government and the configuration is actually quite a different thing from the numbers to get legislation through the House of Commons,” he said.
“Don’t forget in the last House of Commons we’ve just had you had a government which hasn’t been the only outfit legislating and doing things.
“In a minority government it’s now become a convention frankly that may have been established in the 2017-19 parliament that with minority governments, no longer do you have the situation where the executive is the only proper legislator in town, you will have legislators from the backbenches.
“So I don’t think stopping Brexit is inextricably connected to who forms the government, it really is a numbers game.”
The Lib Dem foreign affairs spokesman backed out of the Labour leadership race when Corbyn won in 2015, in a victory which eventually led to Umunna’s own defection.
“I didn’t think I was actually ready, to be frank”
Umunna dropped out of the race, insisting he did not want to invite intense scrutiny and pressure on his family.
But he revealed he also felt he was not a mature enough politician to take over Labour, and revealed he “never truly felt of the Labour party”.
“I didn’t think I was actually ready, to be frank,” he said.
“I’m not sure anybody who stood in that leadership contest in 2015 was ready or had had time to think about what they wanted to do not just with the party but the country.
“Particularly the people who had served in government - you do not have the headspace to think what you want to do and the direction you want the country to go, and it showed.
“Because of course Jeremy Corbyn had had the time, he’d had three decades.”
But he backed David Lammy, a fellow Londoner and People’s Vote supporter, to take the reins at some stage.
“I think David would be a good leader of the Labour party, I think he’s really found his voice.
“And I think he’s an illustration, because when he came in in 2000 he just went up the ranks very, very quickly. A bit like me, actually, it caused a lot of resentment against colleagues who briefed heavily against him.
“That’s in the Labour party never mind in other parties.
“And I think you can see how he has grown, I have tremendous respect for David, I think he’s a fantastic politician.”