In the UK, it is not common for postdocs and entry-level lecturers to negotiate their salaries. This is different from the customs in the USA and some EU countries.
In the UK, the starting salary of a postdoc or a lecturer would normally be set up by HR in consultation with postdoc's PI or lecturer's HoD. As a postdoc, if you want a better offer, you have ...
Read the agreement between your university and the union (presumably UCU) if applicable. It's boring. This defines what you can request.
Read benefits information on the HR website.
Read visa rules on the government website.
Figure out your preferred start date.
Estimate your relocation costs.
Find out what local taxes are.
Find out local housing costs ...
Congrats! On top of what you already mentioned, my list contained:
Is there an assistant who can help with settling down? Like, helping with housing, taxes, reading payslips. etc.
Healthcare. How does it work? When will be available? And everything related.
Are there any links to the international community of the university members?
Don't over plan, ...