“We established a good relationship. We’re grateful for him for making the time… for that dinner,” Sir Keir said.
“We had a good, constructive discussion and, of course as prime minister of the United Kingdom I will work with whoever the American people return as their president in their elections, which are very close now.”
Sir Keir has not met Vice-President Harris, Trump’s Democratic rival.
But he has met President Biden several times since becoming prime minister in July.
Speaking on BBC Breakfast, Reed said UK volunteers campaigning in US elections was “not unusual”.
“It’s up to private citizens how they use their time and their money, and it’s not unusual for supporters of a party in one country to go and campaign for a sister party in another, it happens both ways round and across many many countries.
“But none of this was organised or funded by the Labour Party itself, these are individual people making their own choices as they are free to do.”
Reed highlighted the UK’s “longstanding special relationship” with the US, adding the Labour government would “work closely with whoever the people of the United States elect as their president in November”.
He said Sir Keir had “a very useful and respectful dinner” with Trump in New York last month, in addition to meeting President Biden in the White House.