You can get a free SIM card from Sainsbury's. They are one of the low cost networks in UK. You just need to fill up the online form with your details and address and they will post you the free SIM card to your mailing address. Upon arrival of the SIM card, you can choose activate the cheapest call, SMS and internet bundles.
Click on “GET IT HERE” button and you will be taken to the Sainsbury's free SIM card request page. Scroll down and fill out the form and submit it and it will arrive within 5 days.