If you are looking for a mobile phone provider in the UK that would support using a mobile phone SIM account for incoming calls only without a contract, then you should consider GiffGaff which is a subsidiary of O2.
Most UK PAYG SIM only packages will allow you to use your account for incoming calls only for a limited time of anything between 3 to 6 months but require you to either topup or make a chargeable call/text once every 90 or 120 days to keep your account active, however with GiffGaff as long you have incoming calls your account will remain active.
If you have never heard of GiffGaff, you mght be wondering is this a con? The reason why GiffGaff doesn't demand you topup every 3 or 6 months is that every mobile network owner gets paid a fee for terminating a call, so as long as people call the mobile phone the network is making money, but the bigger networks are greedy, and make more money by getting people to topup and force them to make calls.
GiffGaff even has a monthly bundle especially designed for people who get a lot for incoming calls, for a fee of £5 you get 60 mins and 300 texts and for every complete minute of incoming call you get, they add an extra minute to your call allowance.
So if you have an unlocked mobile phone or an O2 iphone, then for a one off SIM activation fee £10 (you get £5 extra credit if you use this link), you can have an incoming calls only mobile phone package. As an added bonus, you can call freephone numbers (0800 or 0500) free from your mobile phone on this network, great for car breakdowns while out and about. No other network in the UK offers this!
If you have a locked mobile phone from a UK network provider, check out the free GiffGaff Guide to phone unlocking.