You bill them for your time and they pay your invoice. You pay your tax at the end of the UK tax year to the UK.
You should be paid more than you are now, as you won’t be paid for holidays, sick pay, etc. They won’t have any obligations for maternity, parental leave, redundancy, etc.
It used to be SUPER desirable to be self employed as you pay less tax in the UK and you don’t need medical coverage in the UK, but they are raising the taxes in line with standard employment so it’s not as desirable.
It’s a great option to tie you over once your visa is approved though!