Jeremy Corbyn has told his MPs he is “confident of a good result” in May’s local elections as he addressed the party for the first time this year.

The Labour leader pointed to the latest opinion polls as evidence that “the gap is closing” with the Conservatives but acknowledged there was a “job of work to be done” to convince people of Labour’s message.

Ipsos Mori has the party up two points to 33 compared with the Tories on 39, while YouGov has Labour up one on 30 compared with the Conservatives on 37.

“In the byelections in local government this year, Labour is doing significantly better than the Tories and Ukip so we go into 2016 working hard and confident of a good result,” he said.

Jon Trickett, the shadow communities and local government secretary, said there were areas of England where Labour will make gains in the local elections and others where it will have to defend its position. He also asked Labour MPs not to do anything that might damage the party’s chances in local elections, which will take place on 5 May.

Although Labour is trailing in the national polls, the main opposition party – be it Labour or Conservative – has not lost seats in any set of local elections since 1982.

Despite Corbyn’s confidence, the party is already managing expectations about May’s result behind the scenes. Labour sources frequently point out that the council seats up for re-election were last fought in 2012, which was a high point for Labour in the local elections and its best performance for about a decade.

Success in local elections is vital for Corbyn as his critics in the parliamentary party could seize on an underperformance to challenge his leadership.

A Labour spokesman said it was a “warm and professional meeting”, although there was also a “robust discussion about the challenge that Labour has”.

Some MPs were unhappy that Corbyn did not reappear to take questions after a break for voting in the Commons. It is understood he had to head for the ITV studios to film a programme with Tom Bradby.