Self employed in the UK, can I use that in Malta?

Hi everyone!
My name is Erika, I am a new member at this forum and I would like to ask some questions, please if you know the answer then do reply!

I and my boyfriend are living in London, and though we are not residents of the UK, we both hold EU passports. I am an artist working  with ceramics and I want to register myself as self employed in the UK, to be able to collaborate with shops and galleries.

My boyfriend was offered work here, so we had to move here (very recently), but as beautiful as this country is, the gloomy weather is killing me (I lived in the north 6 months already a couple of years ago, and boy was it windy and rainy). We come from separate countries and we both find it hard to live in each other's, so we have decided to find a place we'd both call home.

I was wondering about the legalities in Malta. Was it possible to be registered as self employed in the UK and then work as such in Malta, or would it be a better idea (if at all possible) to register myself in Malta?

My boyfriend will hopefully find work as a fitness instructor/personal trainer and then I understand that employers can ask a work permit for their employees...If you know of any jobs of this sort, that would also be greatly appreciated.

At this point all I really want, is to be able to do what I love and see the sun! I'm thinking that is not too much to ask for

If you have any other helpful information, that you consider relevant, I'd be more than happy if you would share!

Oh and send some sunshine over to my corner of the world please...
greeting to you all,
Erika