A good way to start dabbling is Halifax.. they pool investments (share builder) can to lower cost once a week to cost £2 per trade.. still 12.50 to sell when ever.
If you want to drip in regular small amounts to build a nest egg and build experience of the markets it may be a good idea.
There also may be accounts that free trades for initial period. Remember you'll still have stamp duty either except for AIM listed shares that are exempt. These are less mainstream companies that are inherently more risky, some well known though like ASOS.