You should visit the London Stock Exchange web site
http://www.londonstockexchange.com/
There is advice there as well as lists of brokers. Different brokers offer different services but it sounds like you are looking for an execution only online service. You should not deal with a broker who is not listed there.
Pitfalls to avoid include "penny" shares, unsolicited phone calls offering exciting oportunities and acting without properly thinking something through.
A little while ago I predicted here that the footse index would test its recent lows again without falling below them. If this is right, there will be good buying oportunities over the next weeks but you should not invest in anything that you don't understand and you should not use money that you can't afford to lose.
There are plenty of publications in newsagents offering up-to-date advice. I like Investors Chronicle.