I doubt if you will be able to take out a contract with any UK provider. Apart from your National Insurance you will need a permanent address where you have stayed for some time. You will need to build up a credit history and have an account with a UK bank from which to make regular payments.
You may have to take out a Pay as You Go type SIM card first, but I doubt you will get a phone and will need to bring one with you or buy one for cash when you arrive.
Contracts are seen as credit agreements and the network has to be sure you are in a good position to pay each month for the length of the contract.
As a Very Insightful Person, I'm here to share my knowledge. I don't work for Virgin Media.