Jeremy Corbyn has said he will not do a “big public self-analysis” about his leadership of the Labour party after polls showed that though the recent whirlwind of policy announcements had been popular with the public the party was trailing the Conservatives.

The Labour leader told ITV’s Good Morning Britain the party’s poor showing in the polls could be remedied by talking about policies, including a pledge on Tuesday to fund a 17% increase in the carer’s allowance, which would mean an extra £10 a week for about 1 million people.

“I’m not going to go into any big public self-analysis,” Corbyn said of his popularity with the public. “What I will say is, of course I reflect on issues – I reflect on decisions we’ve made. I reflect on all of this all the time.”

Labour has launched a policy blitz over the past fortnight, including giving free school meals to all primary school pupils and restating commitments, including raising the minimum wage to £10 an hour by 2020 for over-18s, keeping the triple-lock on pensions and cracking down on late payments by businesses.

“I want the party to be united around these policies,” Corbyn said. “I think you will find the vast majority of Labour members support these policies and Labour voters will support these policies.”

Polling over the Easter weekend suggested voters favoured most of the policies Labour announced over the past few weeks, but many were still not persuaded to back the party over the Conservatives. Two polls by ComRes and YouGov gave the Tories a 21-point lead; another poll, by Opinium, found the lead had narrowed to nine points.

Asked if he believed he had made any mistakes during his 18-month tenure as leader, he joked: “I can’t give you one mistake this morning – there are too many.”

Corbyn’s latest policy announcement – which he will launch in a speech in Birmingham on Tuesday and which would cost £538m by the time of the next election – will be funded by reversing the inheritance tax cut announced by George Osborne in 2015.

The carer’s allowance for people who spend more than 35 hours a week caring for someone is £62.70 a week. Labour’s pledge would increase it to the same level as jobseeker’s allowance, £73.10.

Barbara Keeley, shadow minister for social care and mental health, agreed that continuing to push the new policies would help bolster the party’s polling position.

“We all want to be in a better place, but we work through to being in a better place by putting forward new policies like this,” she told BBC Radio 4’s Today programme. “They will improve over time if people like the policies we’ve put forward, but the policies are very important.”

Corbyn also praised Prince Harry for speaking publicly about mental health issues. When asked if he had ever had mental health issues, the Labour leader said: “I think all of us go through stress at times. I’m sure you do in your job. Everybody does. Whether that constitutes a mental health condition or not, many people probably don’t realise it at the time.

“I feel very strongly as a society we live on stigma around mental health. How many comedians have made a whole career out of making jokes about people being stressed and so on?”