Exactly the same proportion of voters believe there should be a second referendum on Brexit as think the UK should leave the EU without a deal, according to the latest Opinium poll for the Observer.

The survey shows the country split down the middle, with 43% supporting a delay to Brexit in order to hold a second public vote and 43% believing the UK should simply quit without any agreement with Brussels.

If a second referendum were held with the options of accepting Theresa May’s deal or remaining in the EU on the ballot paper, 46% said they would back remain, against 36% who would vote to leave on the terms of the prime minister’s proposal.

The poll comes after a dramatic week of voting in parliament when the prime minister’s deal was rejected for a second time, by 149 votes. MPs also voted to rule out no-deal and to extend article 50 by at least three months.

The figures will encourage remain supporters ahead of a mass demonstration and march in favour of a second referendum that will take place in London on Saturday 23 March.

Despite the government’s troubles over Brexit, and cabinet splits on the issue, the Conservatives (on 38%) hold a four-point lead over Labour (34%) with the Liberal Democrats and Ukip both on 8%.

May’s ratings on her handling of Brexit remain dire (-30%, when the proportion who disapprove of her handling of it – 56% – is subtracted from the proportion who approve – 26%).

But Labour leader Jeremy Corbyn fares even worse with a net rating of -46 (62% disapprove, against 16% who approve).

The poll shows that if the UK is still a member of the EU on 23 May, more British people would find voting in the European elections unacceptable (43%) than would be relaxed about the idea (38%). If the UK were to elect a new batch of MEPs, 13% say they would not vote, 19% would vote for Labour, 19% for the Tories and 11% for Ukip.

A fortnight ago May held a 15-point lead over Corbyn when voters were asked who would make the best prime minister. This has fallen slightly and is now an 11-point lead.