You'll need a mobile phone while in the UK.

If your current mobile phone uses a sim card, then an inexpensive option would be to:

1) call you current mobile phone company and request instructions and SIM unlock code for your phone

2) Get a Pay-As-You-Go SIM card in London with a London phone #

I used 3Store last year for my Nexus tablet, and I was happier with them than I was with T-Mobile or EE.

Check out the info I've included below.