Labour is facing the prospect of damaging setbacks in England, Scotland and Wales in the May elections, members of the shadow cabinet have been told. The party could lose around 200 council seats in the English local elections, as well as being pushed into a minority in Wales and going backwards in the Scottish parliament, said Patrick Heneghan, Labour’s election director, in a presentation.

According to one report, members of the shadow cabinet listened in “stoical silence” as Heneghan set out the party’s prospects in the elections, due to take place on Thursday 5 May. The only good news for the party came from the mayoral contest in London: a recent poll gave Labour’s Sadiq Khan a 10-point lead over his Conservative rival, Zac Goldsmith.

Heneghan’s analysis was in line with opinion polls and local election forecasts that were already in the public domain. In the last comparable set of local election results, in 2012, the party gained more than 800 council seats. This time, as well as losing about 200 council seats, Labour could lose control of up to six councils, the shadow cabinet was told.

Labour is in power in Wales, holding half of the 60 seats in the Welsh assembly. But on current trends the party is expected to lose seats in May, meaning that a minority Labour administration could find itself dependent on the support of smaller parties.

And Labour seems to be on course to lose all the constituency seats it holds in the Scottish parliament, meaning that it will rely on gaining representation at Holyrood through the regional seats that act as a top-up under Scotland’s proportional voting system. In 2011 the party won 37 seats at Holyrood, including 15 constituency ones. According to recent polling, the figure could fall to 26.

A Labour spokeswoman refused to comment on the briefing, saying the party did not discuss what was said at shadow cabinet meetings.

A poor performance in May would embolden Jeremy Corbyn’s critics within the party, even though some of Labour’s problems predate Corbyn’s election as leader. In a speech last weekend, Michael Dugher, who was recently sacked by Corbyn as shadow culture secretary, said the May elections would show whether the party was heading “in the right direction”.

Dugher said: “We will be able to see what the answer is to that big question: after last year’s devastating defeat in the general election, are we getting back in touch with the country or are we moving even further away from the public?”