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.