The Sky News presenter confronted Miatta Fahnbulleh after official figures showed the controversial policy could push 100,000 old people into relative poverty.
Chancellor Rachel Reeves announced shortly after getting into power that the universal payments, which are worth up to £300, would be means tested from now on.
That means that around 10 million pensioners will no longer receive the annual payout.
Fahnbulleh, the energy consumers minister, said: “The chancellor had to make a tough call on winter fuel payments, but we’ve been really really clear that we’re going to do everything that we can to support vulnerable households.”
But as she insisted the government was doing “everything we can” to help people, Burley hit back: “You’re not because you’re taking the money of pensioners – you’re not doing everything you can at all.”
The minister said: “We made that decision in order to manage the public finances.”
Burley said many pensioners “might not see next winter unless you help them with their bills – it’s freezing outside”.
She added: “It was a silly silly silly decision to make.”
Fahnbulleh told her: “For pensioners struggling this year, what I’d say is please call your suppliers. They’ve got an obligation to help customers who are vulnerable.”
Burley hit back: “You’ve got an obligation to look after pensioners.”