Status re work

Hi all, we have, unfortunately been obliged to return to the UK to live since the beginning of October (partner’s work, not Brexit) but I have been fulfilling a commitment already made to look after someone while her family is away on holiday.
It got me thinking, would I be able to offer a paid service as live in carer to English people over here who are unable to visit family in UK due to having a dependent relative here in France. I was doing the opposite while I was living in France, i.e. going to England to work, sometimes through an agency, sometimes privately. What would be the legal/tax implications? I am self-employed in England. Anyone know? Thanks.

According to current proposed arrangements, Brits will need a work permit to work in France after transition.