yes of course it would be legal,
Although you may have to check with the local council that it is fine to use your house as an active place of business. I know it it OK to run a business from home, but I'm not sure if it's OK to open up shop in the middle of an estate or whatever.
When fixing other peoples computers you might want to consider some kind of public liability nisurance.
Also know that if you aer setting up as a sole trader, or a simple partnership then you'll be liable for all business debts should the worst happen.