Higher food prices are not because of Brexit. I live half the year in France and the food is far more expensive there. It was always more expensive but it's become increasingly so and they have their own COL crisis just like us. Petrol is more expensive too. And I can find a better and wider range of EU imported food goods in the UK than I can in France, even post Brexit. Everyone is paying more for food, mainly because of Ukraine. USA, Canada, Europe, everywhere.
A return to blue passports was never a reason to vote for Brexit, merely a welcome symbolic part of the overall result.
No change in immigration is another matter entirely though, as is the shameful wasted opportunity to harness all the benefits Brexit could and should have brought us. I still consider the removal of FOM to be a benefit in itself though, so it's all good, just not as good as it might have been.
Although when you add HK and Ukraine into the mix, they were sizeable one-off asylum waves that added to the overall figures shooting up massively for a year or two, which was already on the way down by the time Sunak left office. So it will be relatively easy for Starmer to make it look like he's reduced immigration pretty quickly without actually doing much at all.