Three has a good PAYG tariff of 3p a minute, 2p a text and 1p per mb of data (3G). However three has a reputation for not so good signal, and poor customer support.
What I would personally recommend is the mvno giffgaff. It's 10p min and 6p a text. Alternatively you can buy 3g or 4g goodybags which essentially provide contract like plans but without tying you in to a lengthy contract. There is nothing to sign. You just pay for whatever goody ag and it lasts for a month, you are not bound by any agreement or contract. At the end of the month you just buy another goody bag for the next month.
Here is a link to the giffgaff website for pricing and their goody bag offers. giffgaff.com/goodybags
Also I use giffgaff in my daily carrier and can attest to great uk signal.