I’d say electrolysis would be the best for you. I’ll explain quickly because more information is best regardless-
Laser is hair REDUCTION. It targets the pigment in hairs (melanin), making them far, far less visible in areas successfully treated. As such, it is only suitable for dark hairs. There are different lasers that are suited to different skin/hair combinations, but only a professional can really say what would work for you.
Electrolysis is REMOVAL. Each follicle producing the unwanted hair is treated individually, destroying the ability to produce hair in that follicle. This link explains the different types pretty well http://www.electrolysis.co.uk/?page_id=16 .
Laser is ‘faster’ as in you would have to spend less time actually being treated, but both would probably actually yield results around the same time (laser has to be left about 6 weeks between treatment from what I understand).
I can’t personally recommend anyone for either procedure in London, but maybe make some consultations with BIAE members if you decide to go the electrolysis route. http://www.electrolysis.co.uk/?page_id=767. That’s not to say people outside the institute are not good, but in the Glasgow area I’ve personally found ones with them are better.
Good luck!