Yes. I stuck 5k in last year, in dribs and drabs.
I use a barclays share isa, any capital gains and dividends are tax free. You can now put up to 10k per year in it, more than enough for most people. Allows you to buy shares listed on the LSE main markets but not AIM. I only make occassional trades, so it might not be suitable if you want to do it day to day. You have to pay a fee per trade, although the more trades you make per 3 month period the smaller the fee.
Done it for less than a year, primarily as an alternative to cash isas and their to poor interest rates. Pretty low risk shares with an ethical side - banks, property/house builders and arms companies are my investment strategy, with a bit of tobacco diversification in the near future! Portfolio is currently showing a reasonable return - but I think I bought my first batch of rbs shares at less than 30p.