Tony Blair has criticised Labour’s handling of the Brexit process, saying “trying to keep both sides happy is not possible”.

The former prime minister told an audience in London on Monday evening that although he would be voting for the party on 23 May, “it would’ve been better if we’d been able to fight it in a clearer way”. He encouraged remainers to “vote for one of the other anti-Brexit parties” if they cannot bring themselves to vote for Labour.

The party’s current stated policy is that it would support a second referendum under certain circumstances. Earlier on Monday, the deputy leader, Tom Watson, insisted Labour stood for “remain and reform” and said it seemed inevitable that a confirmatory referendum would be needed for the party’s MPs to agree to any Brexit deal.

On Sunday, the shadow Brexit secretary, Sir Keir Starmer, expressed doubts that a Brexit deal could pass parliament if it did not include a confirmatory referendum, warning that up to 150 Labour MPs would reject an agreement that lacked one.

On Monday night, Blair also threw his weight behind holding another vote. He told the event hosted by the Guardian at the Barbican centre that while Labour were right to accept the result of the EU referendum, another public poll in the event of unsatisfactory Brexit negotiations should have been party policy from the outset of talks.

He predicted the European elections on 23 May would “not [be] good news for the Tories or Labour” and said that, while a no-deal Brexit was “very unlikely”, politics in Britain was “in a unique state of unpredictability”. Politicians had lost sight of the importance of discussing domestic issues such as cuts to funding for health services and police and the lack of opportunities for young people amid Brexit chaos, he said.

“The great irony of Brexit is, the future of the National Health Service is decided in Westminster. The person who’s got the opportunity to do something about knife crime is Theresa May not Jean-Claude Juncker [the EU commission president],” he said. “Brexit’s distractive effect is almost as bad as the destructive effect.”

Blair’s criticisms of indecisiveness extended to the Conservatives. “My view is that both the main parties have made the same mistake if you try and face both ways you end up pleasing no one,” he said. Ultimately though, Labour was an anti-Brexit party and the majority of its MEP candidates had “long credentials in fighting the case for Europe”.

Although he lamented that “it would’ve been better frankly if the avowedly remain parties had been standing under one banner”, Blair stressed it was important for remainers to vote in the election because gains for Brexit parties in Europe could sway the way MPs approach the UK’s departure in parliament.

Adding that he believed that the leave vote had been partially fuelled by legitimate concerns over immigration and globalisation, Blair said the “biggest tragedy” of Brexit was “that it’s the answer to nothing”.