The issue with Sunak's very expensive help for the poorest (and not so poor) is the poorest wont necessarily save it for next winter... they have immediate needs that have to be met, so still wont be able to pay their bills and the wealthier will pocket that £400 and have a nice meal instead.
This was also a flaw in Labour's proposal.
A better way would have scrapped the £400 give away & given the energy companies the money to move the less well off onto lower tariffs and or increased UC... probably the best way.