Yes. I use lloydstsbsharedealing.com to buy and sell shares. There are cheaper options, but it works for me.
Use sites like iii.co.uk or lse.co.uk for tips and forum talk on individual shares... Tip is not to buy and sell too much. Buy, and sit back, for 6 months, or until you hit your target profit, ie 20% or whatever you set yourself.
I managed to turn £4000 into £2600 very quickly, by getting carried away, and selling as soon as the price dropped. Now my £4000 has gone up to £7200 in 12 months.
Bought into BP at £3.06, just at it hit bottom, and they are over £4.50 now.... nice 50% return...
There is a good book, called The Naked Trader, that has loads of info, and tips.