A bill to legalise same-sex marriage in Northern Ireland is set to increase pressure on Theresa May to act, amid the failure to restore power-sharing in Belfast.

A Conservative peer will introduce the legislation in the House of Lords on Tuesday – ahead of an identical move by a Labour MP in the Commons a day later.

The move comes after the Government said it was willing to allow a free vote “on matters of conscience such as equal marriage” in Northern Ireland, despite the matter being devolved to Belfast.

It is almost 15 months since the collapse of the devolved administration at Stormont, with little prospect of restoring it in the near future – making it impossible for Northern Ireland to legislate.

The Love Equality campaign for equal marriage said its preference was for the Northern Ireland Assembly to act, pointing to “overwhelming support” from the public in the province.

But Patrick Corrigan, its spokesman, said: “Without functioning devolution for the last 15 months, we now look to Westminster to legislate.

“We call on the UK Government to introduce its own legislation to ensure equality can now become law for Northern Ireland couples. Discrimination against LGBT+ couples in Northern Ireland can no longer be tolerated.”

The bill is being sponsored by Lord Heyward, a former Tory MP, who said it would be followed by a big petition to be handed in to No 10.

He pointed to John Henry, the brother of Ireland rugby star Chris Henry, who described not being able to tell his brother personally that he was gay as “one of the biggest regrets of my life”.

Mr Henry had moved away from what he perceived to be an intolerant Northern Ireland when he was just 18 years old.

“The strength of public opinion for equal marriage rights in Northern Ireland will be shown by the petition they are due to present to Downing Street later this week,” Lord Heyward said.

The bill will be introduced in the Commons by Labour MP Conor McGinn, but neither piece of legislation can become law without the Government’s support.

Love Equality pointed out that, in November 2015, a majority of members of the Stormont Assembly voted to support equal marriage.

However, the measure was blocked by the Democratic Unionist Party (DUP) using a “Petition of Concern”, a mechanism to veto measures without sufficient cross-community support.

The DUP has called on the Government to impose direct rule on Northern Ireland, if its political crisis cannot be solved soon. Talks broke up in acrimony again last month.

But the Prime Minister has sought to avoid that draconian step, even while setting a Budget to keep public services running smoothly – which will be voted on by the Lords on Tuesday.

Direct rule could make it impossible for the Government to avoid showdowns at Westminster on both same-sex marriage and Northern Ireland’s ultra-strict abortion laws.