They don't do the deal that dbrose mentions but they do have some good ones on atm: https://www.voxi.co.uk/sim-only-plans
Just to add, they don't run a credit check either.
You can get the deal at the moment if you are receiving any type of income related benefits or DLA or something similar. Look up in the site Voxi for Now. They do a check on your bank to make sure you are receiving a payment. If you qualify you get the unlimited for £10 for 6 months. You can also do it on as many accounts as you want.