And trade small at first - REALLY small. Because you'll lose it. Everyone does at first. It won't happen to me. Oh yes it will! Sorry, not being arrogant, just realistic. Ask any trader who's been in the game a while.
Paper trade with City Index or Capital Spreads for a while. You can open a "dummy" account with these guys and they'll give you 10k of monopoly money to play with. See how you do for a few months. You can afford to frighten yourself this way (like using a flight simulator instead of trying it in a real airplane).
If you want to jump straight in, Finspreads will let you open an account and trade at 1p/point for the first 8 weeks (but you can't place stops on less than 50p/point, as I remember). This way you risk real money -- and that will affect your psychology -- but without risking much.
For spreadbetting, all these firms are OK.
Good luck -- and another thing -- only do it if you enjoy it.