What do actually want to connect it to the internet for? If it's simply to watch catch-up TV services and things like Youtube, consider a Now TV Box. It will cost you £14.99 for the box alone (which gives you those catch-up services, plus Youtube and internet radio channels, etc) or you can also add in a subscription to other services [see link] for an extra tenner. Even better, buy your box from Asda where you'll get one of the subscription packages included anyway for a total of just £15:
https://www.nowtv.com/box
The Now TV box gives any TV set 'smart' capability without the need for any other device (except, of course, your router). However if you want to stream content from your mobile phone or computer to your TV set, then consider Chromecast:
http://www.google.co.uk/chrome/devices/chromecast/