A vote to introduce assisted dying across the UK could be imminent after Downing Street reiterated that it would not obstruct a private member’s bill on the issue and indicated it would support an MP in drafting it. However, while polling shows that a majority of the public support legalising support for terminally ill people who wish to end their lives, the issue could cause serious divisions across parties, with opinion heavily divided. Keir Starmer has previously said he supports a change in the law, but the justice secretary, Shabana Mahmood, has said she could not back a policy that she described as “a really dangerous position to be in”. Similarly, while a Liberal Democrat MSP is leading efforts to change the law in Scotland with a private member’s bill on the subject, Ed Davey, the Lib Dem leader, is known to be among senior party members who have doubts about a law change. Much of the timing will depend on whether an MP who finished high enough in the annual ballot for a private member’s bill to guarantee some parliamentary time will take up the issue. The MPs who finished near the top have all thus far refused to say what subjects they are considering. It is understood that some MPs who have high positions in the ballot have been told by the government they would be given adequate staff resources to help them if they should choose to adopt the issue for their bill. However, No 10 denied that any pressure was being put on MPs to adopt the idea. A government source said: “Keir’s views on this issue are well known and he has a strong opinion on this. But it would always be a free vote and it has to be up to MPs and parliament how that bill is brought forward.” A Labour MP, Kim Leadbetter, was drawn top in the ballot, followed by two newly elected Lib Dems, Max Wilkinson and Roz Savage, and then another Labour MP, Clive Lewis, in fourth. Jake Richards, another Labour MP, has offered to put forward the idea for his bill, but he finished 11th, a position likely to be unviable for the measure to progress. The government could formally back a bill but this is seen as very unlikely for such a contentious issue. While Starmer backs a change to the law, the health secretary, Wes Streeting, has said he is uncertain about the idea. Mahmood is more vehement, telling the Spectator in May that she could not back assisted dying. “I feel that once you cross that line, you’ve crossed it for ever,” she said. “If it just becomes the norm that at a certain age or with certain diseases, you are now a bit of a burden … that’s a really dangerous position to be in.” During a fringe event on assisted dying at the Lib Dem conference in Brighton on Sunday, Christine Jardine, a senior party frontbencher, said the Lib Dem-led Scottish bill meant the country was “on the brink of historic change”. She said: “The time is coming when it will be impossible for the UK parliament to not address it. Do I want the Lib Dems to be at the forefront of this? Yes.” However, some of her frontbench colleagues are opposed, with one calling the idea of assisted dying “dystopian”. A government spokesperson said: “Successive governments have taken the view that any change to the law in this sensitive area is a matter for parliament to decide. The government has made it clear it will not stand in the way of debates and votes on any legislation brought forward.”