First stop is to Gran Canaria ...! Have been there and done it. Be careful if you're going down via Gran Canaria, though, and check how often the flights are. It used to be just once a week, though the day changed now and again, and if you wanted to come back sooner, you had to fly back via Lisbon, to Madrid, and then back down to Tenerife! After getting to Madrid 12 hours after leaving Sal, we were further away from Tenerife than when we started!
Direct flights from the UK now, though, as Acmar says, and I think the London airport is Gatwick. Flights go into Sal from the UK, if nothing has changed, whereas the Gran Canaria flights go into Santiago.
(There was talk of direct flights to Santiago from Birmingham, but I don't know if they've started up or not).