Today is three years since I got my proper UK work permit. Assuming immigration laws don’t change again (and they’re unlikely to without the impetus of an election campaign), I could apply for permanent residency in another year.
If I got it, I could work anywhere in the UK, without needing a permit. I’d be able to contract, and earn loads of money. I assume I’ll still love working at the museum, so it might be an interesting dilemma.