If you havent yet maxed out your ISA, then its a no-brainer. You get excellent tax rebates and its silly not to take advantage of these before considering self investing in shares.
Note that even if your ISA is maxed out, the economic turbulence means that investing in individual stocks is an intimidating place for beginners right now.
The FSA is also looking at revising the average percentages used for pension, from 7% for adventurous investments, down to 5% or 6%, so there is industry wide recognition that on average the stock market is going to be a little less lucrative than it was a few years ago.
Thats not to say you cant still make a whopping profit, but the chances of you doing so as a first time investor are remote to say the least.
My advice would be to look seriously into some of the social lending sites, where you can still easily get a 7% return with minimal risk. Whilst I do have a portfolio which is performing well overall (I am a very speculative investor), I am moving a lot of funds into Zopa.com, as I am averaging 7% return with a lot less time, effort and risk than the stockmarket.
Whatever you decide, I think its time you thought about consulting an IFA. They can help you understand what sort of risk you are willing to tolerate, which is a very important aspect of investing.