The Conservatives head into their annual conference in Manchester with a 12-point lead over Labour, according to the latest Opinium poll for the Observer.

Labour is up three points to 24% after its conference in Brighton last week, at which it rejected pressure to back an explicitly pro-remain stance on Brexit. But the Tories are on 36% (down one) despite another difficult week for Boris Johnson, during which the supreme court ruled his five-week suspension of parliament to be unlawful.

Worryingly for Jeremy Corbyn’s party, the Liberal Democrats are up three points on 20% and for the first time now have the most support among remain voters. However, the poll shows Labour has gained five points among leave voters compared with last week.

The Brexit Party is down one point on 11%.

Despite Johnson’s difficulties, he is still way ahead of Corbyn when voters are asked who they think would be the best prime minister. A total of 37% of voters say Johnson, against just 16% who would prefer the Labour leader.

The percentage of people who disapprove of Johnson’s handling of Brexit has risen slightly from 41% to 43% in the past week, with 37% approving , the same as last week. Corbyn’s approval rating on Brexit has improved slightly, though from a very low level. Some 60% of voters disapprove of his handling of Brexit (compared with 63% last week), against 17% who approve (up three points from last week).

More voters (49%) believe Johnson should obey the law and seek an extension to Brexit if no deal has been reached by 19 October, than the 34% of people polled who believe he should refuse to do so. Among remain supporters, 80% think he should comply with the law and seek an extension, while only 21% of leave voters think he should do so.

Adam Drummond, head of political polling at Opinium, said: “Labour’s rough start to their conference doesn’t seem to have affected their position in our poll but their updated Brexit policy may have done. Although most voters still describe the party’s position as ‘unclear’, they have slipped to second behind the Lib Dems among remainers but gained some support among leavers.

“However, not falling back is not the same as moving forwards. Despite the overall Tory lead falling slightly, Labour remain more than 10 points behind and Boris Johnson’s lead over Jeremy Corbyn as best prime minister is above 20 points.”