A tax payable regardless of whether or not you are a successful investor is stamp duty. A charge of 0.5% of the value of share purchases is levied at the time of purchase. The tax is automatically added to the bill that you receive from your broker.
Some people get quite hot under the collar about stamp duty, saying that it discourages investment in UK shares, is unfair because it is not based on income, eats into pensions and makes the cost of raising equity capital greater for companies. The government raises around £3–4bn per year from it and has shown little interest in abolishing it.