You " want to buy shares" are "not interested in a speedy return" and "want to go to the AGM". Sounds as though you have your priorities wrong.
Why would you want to go to an AGM of a company that is giving you a slow return... I'd prefer more % growth than coffe and sandwiches.
First of all you are buying shares, surely the main reason of buying shares is to make money... the shares hopefully will increase in value and possibly give you a ever increasing dividend... and then at some time in the future, you will be able sell them for more money than you paid for them ... a lot more money ... or why invest in the first place ?
Why would you ask the bank to do it for you, they charge an initial fee plus a percetage of the value of the stock purchased not to mention stamp duty. "Banks are bad advice" I'd say...
... if you are confident enough to select a specific company to invest in (quite a risky attitude I'd say .. all your eggs in one basket) why not do it yourself and cut out the middleman.
I do it a few times a week using
http://www.hl.co.uk/ and just pay a set fee £11.95 plus 0.5% stamp duty.
If you just register with them you can set up a virtual portfolio and invest imaginary money and see how it all works. In one click you can buy or sell your virtual stock. It's not as complicated as you might think and it wont cost a penny... and you will learn how to buy and sell shares. With live pricing on their site you can see when a price has gone up/down, and then buy in an instant possibly saving you money.
It all works well and I can thoroughly recommend them.
Dont go to the bank, they cant react as quickly as you can if it all goes wrong ... and I can promise you .. it will.
If you are doing it yourself, you can be in and out of the market in seconds. Long before you wait in a queue on the phone, for the bank to eventualy tell you their systems are playing up.
If you only take one point from this remember .... Nobody will look after your money like you will you would ... least of all the Bank !