I think I understand what you're trying to achieve. You just want to see how it "feels" to own a share, right? To go through the process of buying and holding, and eventually selling, be it at a loss or at a gain.
Frankly, my primary advice is: Just do it on paper! Just decide, for whatever reason, which stocks to buy, in what amount, subtract 1% for commissions (I'm intentionally staying on the higher side here), and keep track of the price changes daily.
Instead of doing it on mere paper, some brokers offer you a demo account where you can practice your paper trading in the same way you would use a live account. As far as I know, Interactive Brokers and Saxo Bank offer such demo accounts, go look around on their web pages.
The problem about doing it for real is that many of the better brokers, such as the two I mentioned, have relatively high minimum funding limits. You need to send a few thousand pounds to your brokerage account before you can even use it. Of course, you don't need to invest it all, but still, the cash has to be there.
Especially for some younger and inexperienced investors, this can seduce them to gambling most of their money away. Which is why I would not advise you to actually invest in this way. It will be expensive but if it's just for trying it on one share, use your local principal bank for the trade.
Hope this gets you started!