I buy my stocks and shares using two accounts, one with Abbey/Santander and one with Nat West. Santander do not let you trade in a company name, only individuals can trade, but Nat West will deal with both so do bear in mind where your funds will be coming from.
It takes two to three weeks to get an account set up whilst the banks make sure you are not a drug baron and generally make an easy job look extraordinarily difficult but it doesn’t cost anything so if you are thinking of buying stocks and shares at some point in the future I recommend that you set an account up now whilst you are not in a rush. If you want to trade on the US markets as well as UK markets you will need to fill in an extra form (W-8BEN) so make sure you ask for this option so that you are not limited later on.
If you trade on line it costs about £15.00 for each trade. Trading on the telephone is much more costly and so should be avoided if possible.
You will find slightly cheaper stock brokers (there are hundreds on Google) but I have bank accounts with these two companies and I like the interface, especially the “portfolio” section which keeps a track of all your stocks and whether they are showing a profit. All good fun and saves you doing all the leg work. One click of a button and you can see how your portfolio is performing 24/7.
I recommend that you opt NOT to take physical possession of your share certificates but to let the stock broking company keep hold of them for you. It speeds up transactions and at least you know where all your certificates are – especially if the house burns down.