Keir Starmer has said the largest donation to his Labour leadership campaign has been the £100,000 from a like-minded lawyer that he has already declared, as he came under attack from rival Rebecca Long-Bailey.

The pair appeared in separate interviews with the BBC’s Andrew Neil on Wednesday, and Starmer was challenged over the source of his funding.

He said he was complying with Labour’s rules for declaring donations and, after being repeatedly pressed by Neil, said the £100,000 contribution – details of which were published on Tuesday – was the largest he had received.

That donation came from Robert Latham, a fellow barrister. “Nobody’s given me more than £100,000, that biggest donation went up yesterday or the day before,” he said.

Long-Bailey’s campaign has repeatedly sought to cast aspersions on the financial backing for what they argue is Starmer’s very well-funded campaign. She told Neil: “I think there’s always an assumption that you don’t get nothing for nothing in this world. And those who donate to your campaign will expect to be repaid in some way in the future.”

Long-Bailey also claimed Starmer had not yet given sufficient details of what his policies would be if he becomes Labour leader – despite the frontrunner having published a 10-point list of “pledges”.

“I don’t know what Keir’s policy ideas are, if I’m honest. I know he says he wants to adopt the same values that the LP [Labour party] has, but what does that mean in practice?” she said.

“I hope that he keeps to our values and our principles. I think we need to see more detail. We need to see more meat on the bone, in terms of what Keir believes in – and indeed about all of the candidates.”

Long-Bailey was questioned repeatedly by Neil over her role in helping to create contracts for the NHS under the private finance initiative (PFI), when she worked as a lawyer in Manchester.

She said PFI was “the only game in town” at the time; and that she had become an MP to try to change what she called “the intricacies and the insidious nature of PFI”.

Long-Bailey, who is widely thought to be Jeremy Corbyn’s pick to replace him but appears keen to shrug off the label of being a continuity candidate, refused to repeat the 10/10 score she gave the Labour leader in an interview just after the general election.

“That was quite a cheeky interview, and I was asked what I thought of Jeremy and I’ve always said that Jeremy is an honest, decent, principled man. But we did face the worst defeat that we’ve ever seen as a Labour party.”

She said she had given him full marks, “as a person: and I’ll always give Jeremy top scores for the decent human being that he is”.

But she added: “I’m not going to mark anybody out of 10, it’s not top trumps we’re talking about here. We’re talking about the reasons for our defeat, and they were manifold.”

Starmer defended Labour’s Brexit position at the general election – and claimed that “gritty” conversations in leave-voting areas had convinced him that he could win back such seats for Labour.

“Once we’ve got beyond the gritty conversation, and I’ve said to people what are the two or three things you really want me to look at on the train on the way home, they’ve said we need infrastructure and transport, we need jobs with real dignity and security, and we want decisions made by us,” he said.

He also claimed his argument for free movement to be restored after Brexit would resonate in such communities.