Dolphin Finance
Guaranteed Finance do not offer mobile phones with no credit check, but offer a guaranteed SIM card only option which is available for a fee of £25 as well as a £5 admin charge. No credit checks are performed on this SIM card, but you will need to verify your identity by sending in your proofs of address and identification.
Guaranteed Finance are part of the G Finance group which act as affiliates and agents for a number of finance websites which provide credit to people with adverse credit history.
No credit checks are required to sign up for their SIM card, but you are required to send proofs of ID and address and have use of an existing credit card.