The UK will be hit by a "tsunami wave" of red tape and bureaucracy because of Prime Minister Theresa May's "hard Brexit" plan, Nick Clegg claimed on Tuesday 2 May.

The former deputy prime minister said the Conservative premier's decision to curb immigration and not seek full access to the EU's single-market will mean "hassle and expense" for the more than three million EU nationals in the UK.

"I don't think there's the remotest prospect of some mass deportation of EU citizens in this country back to Europe or UK citizens elsewhere," Clegg told his supporters in Westminster, London.

"That's not the risk. The risk is that this government at some point will have to make a distinction between the acquired rights of EU citizens who have been here up to a certain point and the diminished rights of those EU citizens wanting to come to here after a certain date.

"You cannot make that distinction – between rights proceeding a certain date and after a certain date – without inventing an absolute tsunami wave of red tape. Similar, if not identical, to identity cards. What EU citizens face in this country is at first uncertainty, then hassle, expense, red tape bureaucracy and paperwork."

The Liberal Democrat MP accused Conservative Brexit backers of being hypocrites over the issue because they warned against "foreign red tape" during the EU referendum campaign last year.

Clegg also warned that households across the UK face a "hard Brexit squeeze", while the government had "maxed out its credit card" on splitting from the EU.

"This means, in turn, that any additional money for schools and hospitals cannot come from borrowing – it will have to come from further cuts to public services, or from higher taxes," he said.

"In other words, the cost of Brexit will be borne by you. This is why the Conservatives look like they are going to have to scrap commitments on tax and National Insurance, and end the triple lock on pensioners."

Clegg's speech, his first major intervention of the general election campaign, comes amid a row between Downing Street and Brussels.

The dispute was apparently triggered when EU Commission President Jean Claude Juncker had dinner with May and Brexit Secretary David Davis in London on 28 April. Juncker reportedly warned German Chancellor Angela Merkel that May was living in "another galaxy" over the two-year-long negotiations. May, meanwhile, dismissed the reports as "Brussels gossip".

But Clegg, a former MEP, said the account sounded "plausible. A British government talking to itself doesn't surprise me."

The latest YouGov poll, of more than 1,600 people between 27 and 28 April, put the Liberal Democrats on 11%, behind Labour on 31% and the Conservatives on 44%.