The continued staff shortages would seem to mean that it's not simply an issue of pay, and there aren't enough Brits willing to do those jobs.
From what I've read (and take this with a pinch of salt) there are a lot of licensed HGV drivers in the UK who don't drive anymore, with common reasons being long, unsociable working hours, management that treat you like dirt, shitty rules around where they can park to take rest stops with substandard (typical everywhere in the UK...) facilities, and pay that hasn't risen in decades.
This, combined with not enough younger folk taking up the job, along with Brexit, has led to a shortage
The easily exploitable workers aren't available anymore, so the companies who exploited them will have to change their exploitation habits if they want to fill their positions from the remaining labour pool.
Of course a landed citizen isn't going to sign up to be treated unfairly if they don't have to, they're not as desperate and therefore not as exploitable. I imagine they're reading the terms of employment on these positions with disgust, and so they should.
And if, lets say, the corporations will now have to pay double for UK citizens to drive the gas delivery trucks. Wouldn't that raise the gas prices quite considerably?
The world outside the UK is working pretty well with labor import. Even a certain US ex-president was speaking about how bad it was, while he was requesting hundreds of low cost work visas for his vineyards (got to keep costs low...)
This suggests that doubling the pay of the truck drivers would make a much less than 2% increase in pump prices.
Sure, cities will be wealthier than the regions, but ultimately a city in Romania and a city in sweden, infrastructure and education being also equalised through structural funds, should present equal opportunities.
Completely disregarding the language barriers, which are quite extensive so practically freedom of movement would be easy for corporations to use the benefits but not the wider population even if you neglect family ties.
These questions need to be answered and I don't think the educational elite has an answer without painting flowery pictures not too many might be inclined to believe.