The shadow secretary of state was warned not to party too much as the Conservative party suffered a double bruise in the recent wakefield and Tiverton and Honiton by-elections.
Mr Lammy suggested the Tory losses were a signal that the electorate is shifting against the Conservative leadership and towards support for the Labor opposition.
Sky News channel Trevor Phillips was quick to highlight the results in Tiverton, where the Labor party lost significant support to the Liberal Democrat election campaign.
Mr Phillips suggested that the Labor party would likely not see the expected expansion of voter support in a general election and therefore be unable to succeed the Conservative government.
On Sky News, Mr Lammy said: “The result represented a 12.7 percent turnaround from Conservatives to Labour.
“We will not form the next government unless we convince people not to vote Conservative and vote Labour.
“That’s what happened in Wakefield and if that result were to be repeated across the country I would be Secretary of State and Labor would form the government.
“It was an excellent result, we have to win the seats in those so-called red wall zones that we lost in 2019, we have to pick up all over the country – very happy with that result on Thursday.
Mr Phillips replied: “Well, in theory it’s great, isn’t it, and I think you’ll recognize there that the odds of that happening nationally, in every constituency, don’t seem so good.
“For example, Tiverton, you came second there in 2017 and 2019.
“This time the Conservatives were largely defeated because you lost your deposit.
“It doesn’t seem to me that given these results, you’re actually on track for that win.”
Read more: ‘Never gonna happen!’ Lammy mocked over Labor victory in Scotland
The Labor MP hit back, replying: “Trevor, we did well in the local election, we did well in Wakefield, the Tories lost in Tiverton.
“Of course there were Labor voters there who had the Liberal Democrats slowing down their vote so they could see the back of the Conservatives.”
Mr Lammy acknowledged that in Tiverton, traditional Labor voters had shifted support for the Liberal Democrat party as the Labor candidate, Liz Pole, won just 3.7% of the vote.
He added: “This cycle, this Wakefield result, Tiverton and basically the local elections are people turning away from the Conservatives, so the story of the evening was that this was indeed a very, very sorry night for the government. – Labor is one of its way back.”
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