The shadow international trade secretary, Barry Gardiner, has said parliament’s refusal to deliver Brexit has led directly to the surge in support for Nigel Farage’s Brexit party, and is allowing him to dictate what the departure terms should be.

Gardiner, who is among those on the Labour frontbench most sceptical about the idea of a second referendum, criticised the former prime minister Tony Blair for recommending in an Observer opinion piece that voters could opt for anti-Brexit parties in the European elections on 23 May.

“People in this country are angry, they’re angry that the referendum result has not been delivered on by a incompetent government,” Gardiner told Sky’s Sophy Ridge on Sunday show, pointing to polls indicating major support for the Brexit party.

“And there’s a protest that is being signalled by those figures, 34% saying they would go for the Brexit party. There’s no policies in this party, just one.”

Farage has argued the UK must leave the EU without a deal. Gardiner accused the former Ukip leader of seeking to “redefine what the referendum was about”, saying: “The referendum was about leaving the EU. At that time, there was no talk of no deal, there was no talk of going onto WTO terms.”

Asked if his views showed Labour was now an officially pro-Brexit party, Gardiner said the bulk of its MPs had backed remain in 2016. “But when that referendum came in, we said, ‘Look, we made you a promise that what you decided is what we would do’,” he said.

This promise was behind Labour’s decision to join cross-party talks with Theresa May aimed at reaching a consensus on a departure plan.

Gardiner expressed scepticism the discussions could succeed given May’s imminent departure, saying: “We don’t know at this stage even if we could negotiate a deal, what we don’t know is whether the successor to Theresa May would actually deliver on it, and that’s one of the big sticking points that we have.”

Two government ministers defended May on Sunday, with the prisons minister, Robert Buckland, saying the prime minister should, as planned, remain in No 10 until a Brexit deal is passed. “I don’t think she needs to say any more about that,” he told Ridge.

The education secretary, Damian Hinds, offered support for May against criticism from the recently sacked defence secretary, Gavin Williamson, of her decision to open talks with Labour.

“What’s the alternative?” Hinds told BBC One’s The Andrew Marr Show. “We have to find a way through and that means we have to have a majority. I think she’s done a remarkable job and no other person in her position would be able to change the parliamentary reality.”

Polling for the European elections shows support for the Conservatives plummeting to 11%.

Buckland said the vote should be seen as “a giant opinion poll as to the merits of Brexit”, indicating a big win for Farage’s party ought to be taken as a sign for MPs to swiftly agree a departure deal.

“I don’t think mainstream politicians can ignore or disregard the frustration of the electorate,” he said. “It’s very clear that there is a great degree of frustration. The question is, what are we going to do about it?”

On the talks with Labour, he said: “I very much hope that something will emerge from that. I think it’s incumbent on MPs of all shades to realise that what we’re dealing with here is a tension between the direct democracy of the referendum, that most MPs voted for, and parliamentary democracy itself.

“We need to resolve that tension quickly. And we have to remember – it is parliament that is in the dock here.”