Labour has said its plans for an immigration returns deal with Europe would focus on safe routes for children with family in the UK amid Tory accusations of an “open border policy”.

Shadow home secretary Yvette Cooper said the party has always insisted routes to Britain must be “capped” as she sought to defend its pledges against attacks from the right.

Formally joining the European Union quota scheme would not be part of the plan because the UK is not a member state, she said.

A vicious political battle has broken out over Sir Keir Starmer’s proposals for closer co-operation with Brussels on immigration, with Rishi Sunak claiming they could result in 100,000 EU migrants coming to the UK every year.

Touring broadcast studios on Friday, Ms Cooper said the Conservatives were “talking garbage” about Labour’s approach because they were failing in their own attempts to stem Channel crossings.

“Unfortunately this is just Rishi Sunak making things up because his plan isn’t working to tackle the Tory boats chaos,” she told LBC.

“We’ve always said that yes the routes need to be capped… We’re not talking about this European quota scheme at all. We wouldn’t be part of that. That’s part of what the Conservatives have made up.”

But she added that the party would seek some form of returns agreement with other European countries, which would see “controlled and managed but safe routes for children who have family in the UK”.

Home Office minister Chris Philp suggested the plans amount to an “open border policy” that would be unpopular with voters.

“I think his policy has no credibility and the British public don’t want to see 100,000 of Europe’s illegal immigrants being shipped over here under Keir Starmer’s open border policy,” he told Times Radio.

Sir Keir Starmer this week used a visit to The Hague in the Netherlands to promise to “smash the criminal gangs” profiting from from small boats crossings the Channel with an anti-terrorism-style international crackdown.

This would involve strengthening serious crime prevention orders – directions that are used to restrict the movement of serious offenders like extremists and drug traffickers – so that they can be applied to suspected people smugglers.

The Labour leader also indicated he could be prepared to do a deal with Brussels that would involve the UK taking a quota of asylum seekers who arrive in the bloc in exchange for the ability to return people who cross the Channel.

Labour will take back control of our asylum system

Hotels, barges and former military sites would no longer be used to house asylum seekers under a Labour government, the party has said, promising instead new staff to cut the current claims backlog.

The party has pledged to recruit more than 1,000 Home Office caseworkers – a 50% increase on current staffing levels.

Expanding on the Government’s deployment of temporary so-called “Nightingale courts” to deal with the pandemic backlog of criminal cases, Labour said it would use a similar idea to create extra capacity to speed up asylum legal challenges.

A new returns unit, again backed by 1,000 staff, would also be created to triage and fast-track removals in a bid to “take back control of our asylum system”.

The party said that once the current backlog is clear there will be no need for hotels, barges or former military bases, which Labour claims are costing taxpayers more than £2 billion a year.

Binning the Tory Government’s Rwanda plan, which is currently held up in the courts, and redirecting the money to fund its new proposals also form part of Labour’s plan.

Taking a hardline stance on illegal immigration will be seen as important to convince swing voters the party can tackle Channel crossings, which have passed 23,000 this year.

But apart from facing Tory attacks from the right, its policy pledges were criticised by a senior union chief.

Matt Wrack, the president of the Trade Union Congress, told the Guardian Sir Keir was in “danger of pandering to right wing Tory rhetoric” on immigration.

Senior Tory ministers have argued that, if a returns agreement with the EU had been in place last year, it would have forced the UK to take 124,614 so-called “illegal migrants” in 2022 as part of a “mandatory fair share” agreement.

According to the governing party’s workings, if Britain was part of Europe’s mandatory share agreement, its 67 million population would mean taking 12.9% of the 966,000 people who applied to the bloc for asylum last year.

The criticisms come despite Downing Street suggesting it would been keen to hold talks about a returns agreement with the EU.

Sir Keir will be in Montreal in Canada over the weekend for a summit of “progressive” politicians ahead of an expected visit to France next week to meet President Emmanuel Macron.

No 10 downplayed the significance of the Opposition leader’s Paris trip, saying it is “not unusual”, but it is widely seen as a bid to appear statesmanlike ahead of a likely general election next year.

Canadian Prime Minister Justin Trudeau as well as former UK prime minister Sir Tony Blair are among those reported to be attending the so-called “2023 Global Progress Action Summit” in Montreal.