Dependent on phone operators you may require different identification proof. Generally the proof of identification tends to be a Passport, Driving, utility bill and maybe a UK bank account for payment. It is easier if moving to the UK to have an English bank account to set up a phone plan.
There are many phone operators to choose from in the UK and this allows you to be selective with the best phone package for you. When you have arrived in the UK you have many options when choosing phones. If your phone is unlocked and can work on local network, you can choose which operator would suit you. Prepaid SIM cards seem to be a better option for many. This is due to the fact that you will still be able to make calls, send text messages and use mobile data with your current phone. This offers more freedom if you plan on a short term basic, as you then don’t have a phone contract that will require long term payment. If however a long term option appeals more to you, then calls, texts and data could work out cheaper under a contract (especially if you use your phone more than regularly.)