Has anyone here purchased a pay monthly mobile phone from an in-store Tesco Phone shop before? If so, what do they ask to see in terms of proof of identity?

Also, I am currently on a Tesco 1 month sim only tariff but want to take out a new contract with them. Does anyone know if they will be able to set it up to keep my own number in store at the same time?

You will simply keep the SIM card you already have. All that will happen is that tariff will change (if applicable) and you will receive a new phone.
Obviously you will be signing up for a longer contract at the same time.

As for ID, I'd think a debit card and a recent utility bill would do. They'd be able to find you on their system with those as proof of who you are.

I assume you mean you want to upgrade and get a free phone as you said you wanted to keep your number?