The food inspection centres I hadn't seen - that is utterly ridiculous, though don't have an i account so can't read the full thing - is that for food safety inspections as well as customs/excise?
On the labour shortages, I do have some sympathy for the idea that the EU exit caused labour shortages, though that'd suggest that it's not currently a problem elsewhere if you're inside the EU, though in reality other countries are still having issues.
https://www.dw.com/en/is-germanys-sk...yth/a-64767762 (no, but a more flexible market could help)
https://www.dw.com/en/trainee-shorta...oes/a-62974599
https://www.nytimes.com/2022/12/23/b...ance-jobs.html
https://www.reuters.com/world/europe...es-2023-02-02/
https://www.infomigrants.net/en/post...labor-shortage
They all seem to want the same thing, which is more migrants - but given it's an EU wide issue, they're often mentioning non-EU sources, so I don't think it stacks up to say it's purely Brexit - whilst it's likely made it worse, it likely would still be an issue.
the other thing is the actual numbers of migrants entering the UK is running at what pretty high numbers, thanks to the success of the HK/BNO & Ukraine resettlement schemes. I think there's more fundamental issues to address here both in the supply of labour and in the demand side of it, with many small fixes needed rather than one big fix being a silver bullet.