The following web sites are designed for booking domestic and international plane travel. I've indicated which ones I've used to book flights.
flights.com - excellent site; used to be called tiss.com; I use it regularly to book flights. (Note that they may rush you to send them a fax of your credit card details -- the details, not the card itself -- just after you've booked. Some of these sites are quite worried about fraud. Most, though not Yahoo, require that tickets are sent to your billing address.)
London is a very good hub to buy tickets from. However, if you are flying into one London airports and out from another, it may be an unpleasant surprise to find that it is not easy to get quickly from one to the other. There are regular high-speed trains from the Centre of London (not always to the same station) to Heathrow, Gatwick and Stansted but the most convenient way to travel (if you are using different airports), if time permits, would be to take a coach to go directly from one to the other. (By the way, Heathrow is also on the London Underground.) Best of all, would be to fly in and out of the same airport.