You will likely be charged a fee each time a broker purchases or sells stock for you. The only time that will not happen is if you have an automatic reinvestment option for any dividends. The way to check my answer is to ask your broker the question. Since you are taking about investing British pounds I am assuming the process is the same there as it is in the USA. The concept of investing money on a regular basis is a great idea, you just need to be careful that the investment fees don't eat into you capital. Use a low cost on line broker with low fees to minimize the impact of the fees or instead of investing monthly do it once per quarter.
Are you surprised? Nobody does business for free. Its all about money
Take care
say if i was to dollar cost average a stock. the first time the broker they will charge me to invest £50 but say after every month i invest £50 will they still charge me a fee to invest more in same stock?