Working from UK to Spain

Hi!

I'm newby in this foro and in the issue of to be a freelance.

Right now I'm working in Spain but I'm going to live to UK in few months. Then I would like to continue working for Spain from UK (remote mode) and also work for UK clients.

It's possible?
I must to be registered in each country?
How I must to do bills for Spanish companies?

Any help is welcomed!