Assuming the rules in the UK are the same as in the US, you basically have 3-tiered choices.
You can hack together a lame feed from things like Google or Yahoo but you absolutely are not getting every tick, if that is what you are after.
A step up from the obvious internet sources are some of the online brokers. Their data is more reliable and timely but obviously you need an account and they have to offer some kind of API. Check into something like InteractiveBrokers.com. They are mostly java centric but offer a Window's based C++ DLL as well. Several other brokers offer similar APIs but IB is excellent in that it covers a multitude of exchanges including, I believe, London. They also make it relatively easy to transfer currencies if that is a concern.
Lastly you have to go to commercial brokers. You can find them easily enough with a search but be prepared to pay a couple of hundred dollars per month minimum.
I think Mark's suggestion of QT is a good way to go for a GUI. Java tends to be adequate for putting up a grid of running quotes but tends to fail in the charting area, IMO.
