Yes. Most of the major banks have an online trading facility as part of their online banking service. For simplicity, trading through the bank you bank with is the most convenient. Commissions vary depending on your status with the bank, the current deal and so on, but with HSBC, for example, they start from around 0.25% (plus various small things like stamp duty, and other minor charges). I think just one extra form (or even just a tick box on the account setup form) is all you need to get started with your bank.
Note that the above doesn't apply if you are a US citizen - most banks refuse to do investment business with them because of the onerous reporting requirements imposed by the US Government.