To purchase financial securities such as stocks, you will need a brokerage account. To do this, however, you will either need an adult co-signer or have to wait until you are an adult. UK law, like that of most countries including the rest of the EU and the US, requires a co-signer for minors to open brokerage accounts. I believe the cutoff is 18. I agree that this is unfair, but it is the way the law is written. When they finally let you vote, perhaps you should try to find candidates who want to expand the rights of young people.
But you may be able to get a co-signer.
Whenever you do open an account, I strongly recommend choosing a brokerage with low trade fees. Currently there is an online brokerage called Robinhood which has no trade fees at all, though I think they may only accept US citizens. But even so there are probably similar no-fee or at least very low-fee brokerages available in the UK.
For the scale of money you are talking about, even a fee of a few pounds per trade can eat away most of your returns. (For example, suppose you make 5% on an investment of GBP 1000, but have to pay a trade fee of GBP 5. That means you paid GBP 1000, but only got 995 in stock; then it rose in value to 1044.75. You sell it and get back only 1039.75. So your net return is GBP 39.75, a return of about 4% instead of the 5% you'd have gotten without trade fees.)
I also recommend that you buy diversified exchange-traded funds (ETFs). While these are not as exciting as short-term trading of individual stocks, buying and selling individual stocks is extremely risky, and most of that risk is diversifiable, meaning that it's just pure risk---it's not actually improving your overall return. ETFs remove most of the diversifiable risk and leave you with only nondiversifiable risk, which is directly related to making higher returns. You could achieve the same goal by buying many different stocks, but buying even 1 share of say 100 different companies (which is what you'd need to realistically diversify) would easily cost tens of thousands of pounds--plus if you have fees, you'd pay a fee for each of 100 trades. ETFs are structured so that you can buy into them with much smaller amounts, only a few hundred pounds, and all in one trade.