Home Secretary Shabana Mahmood has said she is willing to consider “a big increase” in payments to failed asylum seekers to persuade them to leave the UK voluntarily.

She told the BBC this was often “better value for money for the taxpayer” than the cost of people remaining in the country.

Mahmood also defended her plans to start deporting families who have been rejected for asylum, even where this includes children.

The proposals are part of a major overhaul of the UK’s asylum system, which was announced in Parliament this week and has attracted criticism from some Labour MPs and peers.

Speaking to BBC Radio 4’s Political Thinking with Nick Robinson, Mahmood was asked whether paying failed asylum seekers to leave was the right thing to do with taxpayers’ money.

She argued

“I’ve already asked my officials to pilot a small programme where we offer more than we currently do, just to see how that changes behaviour,” she said.

“I haven’t alighted on the full sums involved yet but I’m willing to consider a big increase on what we currently pay and that’s because… that’s often better value for money for the taxpayer.

“I know it sticks in the craw of many people and they don’t like it but it’s value for money, it does work and a voluntary return is often the best way to get people to return to their home country as quickly as possible.”

One aspect of the government’s plans which has proved controversial with some backbench Labour MPs is a change in attitude towards removing families with children.

The government does not currently prioritise deporting families who have been rejected for asylum but under the proposals they could be forcibly removed if they refuse to leave the UK voluntarily.

On Tuesday Labour peer Lord Dubs, who came to the UK from Nazi-occupied Czechoslovakia on the Kindertransport, told BBC Radio 4’s Today programme that Mahmood was “weaponising children” and should think again.

In response to his comments, the home secretary said: “I always listen carefully to what he says but on this occasion I do disagree.”

Insisting she “would never use children as a weapon”, Mahmood said she had a duty to get rid of reasons for putting children on dangerous small boats crossing the Channel.

She said: “There is a perverse incentive there to still travel with your children, maybe put your children in danger, if you know that we would never ever remove a family with children when they have failed in their claim.”

Acknowledging there were specific concerns around the removal of children that needed careful consideration, Mahmood explained she also needed to be fair to British taxpayers “who are footing that bill”.

She added: “It is right that if you’re a failed asylum seeker, the fact that you have a child under 18 is not a reason why you should remain here in supported asylum accommodation forever more.”

Another issue that has caused concern is reports that asylum seekers could be stripped of jewellery at the border when they arrive.

Mahmood insisted asylum seekers would not have any items of sentimental value, such as wedding rings, taken away.

However, she said individuals with a “flashy Rolex” watch, e-bike, car or other high-value assets “should make a contribution” towards the cost of their stay.

She gave the example of an asylum seeker who was being given £800 a month by his family and had bought an Audi.

“He was not required under any of our rules to contribute towards the cost of his asylum accommodation,” Mahmood said.

“Now most British citizens have to contribute towards the cost of accessing the benefit system, and if they have assets that is taken into account when they seek social security money.

“So what I’m trying to do with that change is put asylum seekers on the same sort of playing field that British citizens are on.”