They know that their exact problem description will get to the people who can solve it rather than being filtered through non specialist staff. They know that they will not be put on hold. Apologies for stating the obvious, but a happy customer is a profitable customer - referrals, further business, etc. Anyone considering buying something from a British company will be much more likely to buy if they have web based support available. It is hard enough to get decent customer support from a local company - how much harder is it when one has to deal with time zones, international phone calls, language problems, and cultural differences.
People hate talking to foreigners.
For instance, Americans get nervous with English people. Quite a few Americans would rather go to the dentist and have some teeth pulled out than ask an English person a question and be made to look stupid. On the other hand many English people will happily admit that making Americans look stupid is a favorite pastime. This is a serious impediment for British companies looking to break into the world's largest market. On the other hand, web useage is commonplace in the USA and if you have good web based customer support, you have a good chance of making the sale.