Home Secretary Yvette Cooper has told the BBC the level of “dangerous” illegal Channel crossings is “far too high” but she refused to set out a timetable to reduce the number.

More than 20,000 people have arrived illegally on UK shores since Labour took power, up on 17,020 during the same period last year.

It comes as the Home Office said it was on track to return the highest number of failed asylum seekers in five years, with nearly 13,500 people sent to their home countries since the election in July.

During a visit to Rome, Cooper told the BBC’s Sunday with Laura Kuenssberg show there had been a “bad history” of home secretaries giving pledges on migration they then failed to keep.

Cooper said the four biggest return flights have taken off since July, and that the number of raids and arrests for illegal working had gone up by a third since that time.

Shadow home secretary Chris Philp said the return figures were a continuation of “the upwards trajectory we have been on under the previous government”.

Cooper said restoring order and control to the asylum and immigration system is linked to “restoring respect for the rules, enforcement of the rules, and making sure those returns take place”.

The rise in small boat crossings is largely due to a spike during the month of October, with Home Office sources pointing to a higher number of days during the month when seas were calmer in comparison to last year.

The number of migrants crossing in Labour’s first five months in office is similar to the 20,839 that crossed between July and November in 2021.

Cooper told the BBC: “These levels are far too high, this is dangerous what’s happening.

“Of course we want to continue to progress, of course we want to see the boat crossings come down as rapidly as possible.

“What we are not going to do is deal with this by slogans. Rishi Sunak said he’d stop the boats in a year.”

Labour scrapped the previous government’s plan to deport some asylum seekers to Rwanda in a bid to deter crossings.

The scheme was first announced in April 2022 under Boris Johnson, but it had yet to get off the ground by the time of the election.

Cooper has previously described the policy as a “grotesque waste of money”. Instead, the government says it will attempt to reduce crossings by taking action against the gangs that smuggle people into the UK.

The government announced on Sunday that £8m will be ring-fenced for new technology, including body-worn cameras and fingerprinting kits to “ramp up immigration enforcement operations”.

The new technology will support operational teams as they build cases “against those working illegally in the UK or unscrupulous businesses employing them”.

Biometric fingerprinting kits are set to be given to those on the frontline, which the government says will enable immigration enforcement officers to cross-check detained individuals against police databases “on the spot”.

The home secretary also suggested she hoped to fast-track claims from those seeking asylum from countries deemed safe, and remove them more quickly from the UK, as well as potentially adding more countries to the list of safe places where people should return.

Cooper denied migration had fallen down the government’s priority list, even though there was no specific “milestone” target set by the prime minister.

She told the BBC: “We have made clear border security… is one of the foundations. We have made it clear we need to reduce both legal migration and illegal migration, it is a clear priority for the government in terms of tackling these dangerous boat crossings.”

As she prepared for meetings with Italian Prime Minister Georgia Meloni’s government in Rome to discuss cooperation on illicit finance of the people smuggling trade, Cooper said the government’s approach to tackling illegal migration was “step by step… we are being very clear and straight with people about the complexity of this, because the gimmicks did not work”.

The meeting with her Italian counterpart, Matteo Piandetosi, came at the end of a week of diplomacy on border control.

According to a Home Office readout of their talks, Cooper and Piandetosi spoke about the importance of “taking an end to end approach” when it comes to tackling irregular migration.

The two leaders are said to have agreed to follow-up with commitment from both prime ministers in September to “follow the money” when it concerns the illicit financing of people-smuggling gangs.

Earlier this week, Germany and the UK agreed on a deal to tighten Berlin’s law to make it easier to prosecute those helping to smuggle people into the UK.

Under the new agreement, the Home Office says Germany has pledged to make the activity a clear criminal offence.

Sunday with Laura Kuenssberg airs on BBC One at 09:00 GMT on Sunday 15 December