Asylum seekers would have the right to work after three months of arriving in the UK under a bill introduced in parliament by the Liberal Democrats.

The move on Thursday by the Lib Dem MP Christine Jardine comes as calls grow for a relaxation of the rules.

People seeking asylum in the UK are only allowed to work if they have been waiting on a claim for 12 months or more and can fill a role on the shortage occupation list, which includes positions such as classical ballet dancers and geophysicists.

The Home Office aims to process all initial asylum claims within six months, but 48% go beyond that target.

This means people have been essentially banned from working while they wait months, and often years, for a decision on their claim, living on the £5.39 a day the government provides.

Jardine’s asylum seekers (permission to work) bill, if passed into law, would allow asylum seekers to work after three months of lodging their claim.

It has the backing of the Lift the Ban coalition, which has published research showing asylum seekers blocked from working in the UK could make a net contribution of £42m to the economy if restrictive rules were lifted.

Jardine said: “Right now, banning the vast majority of asylum seekers from seeking employment costs the taxpayer millions in housing and support payments. It also forces people who have risked everything to come here to live on the very periphery of society.

“Being denied the right to work, and to put food on the table for you and your family, is cruel and undignified.

“If passed, my bill would recognise the contribution genuine asylum seekers want to make to our society by allowing them to work after three months of lodging their claim for asylum.

“This change would also allow them to learn English faster and integrate into their local communities. For me, it’s a no-brainer.”

Members of the public would be broadly supportive of lifting the ban on working, according to expansive polling by the thinktank British Future, which found 71% agreed it would help integration if asylum seekers were allowed to work after six months waiting for their claim to be processed.

On behalf of the Lift the Ban coalition, Paul Hook, Refugee Action’s head of campaigns, said: “The majority of the British public think it’s the right thing to do, it would be transformative for people seeking asylum and the idea is widely supported by businesses nationwide.”

The home secretary, Sajid Javid, said last month there were no plans in place to lift the restrictive rules, but he would like to review the ban.

Jardine’s bill is a type of private members’ bill that is introduced without debate in the House of Commons. As with other public bills, their purpose is to change the law as it applies to the general population. A minority of private members’ bills become law but, by creating publicity around an issue, they may affect legislation indirectly.