On the first point, they promised otherwise. Were they lying?

Anyway you can leave the EU politically but remain in the customs union and single market, that is a type of Brexit. Gas is a global market and we are disproportionately reliant on it; have poorly insulated homes and very little gas storage capacity, so we will suffer massively anyway in addition to the economic hit from Brexit.
I mean acting to reassure people and mitigate the effects before the price cap went up again (all our European neighbours acted months ago and this has been effective in the mitigating rising bills, ours have gone up the most by comparison).