The now deputy prime minister donated the powder-blue Marks & Spencer fitted knit jacket to the museum, where it is displayed in a glass case alongside a range of other Labour party memorabilia. "Look, I give clothes away too," she jokes.
Sitting downstairs in the cafe at the museum, Rayner bats away some of the damaging headlines - over donated clothes, staff salaries and bitter Downing Street infighting - that have plagued Labour in recent days, insisting that she is getting on with the serious business of governing.
As the party prepares for its annual conference in Liverpool, Keir Starmer has faced criticism for declaring more free tickets and gifts than other major party leader in recent times, with his total topping £100,000, including clothes donated to his wife, Victoria.
But for Rayner, the important thing is that he did declare the gifts, unlike some of his predecessors in No 10. "Look, the donations rules apply to all of us. Keir is really clear that you have to disclose when you've had donations," she said.
"I do think the rules matter. I've been slagged off for going to Glyndebourne. I've been slagged off for going to Ibiza for four days on my holidays. Am I not allowed to do that?" "I get criticised for doing things.
The fashion brand] ME EM donated me some suits and I declared them and you know, I've donated clothes for charity the other way," she said.
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