Upvote:2
While I can't speak for Heathrow specifically, pay-as-you-go SIM cards are widely available in supermarkets in the UK. They're usually either at the till or behind the counter, so you might have to ask the cashier.
They're usually "free" in that you pay £10 and get £10 of credit on the card. If there is an extra charge, it won't be more than a few pounds.
For pay-as-you-go, I can personally recommend Three, as their default plan is better value than most in the UK. Calls are 3p/min, texts are 2p and data is 1p/MB (so a £10 top-up gets you 1GB of data). However, they don't always have the best coverage outside towns and cities.
To answer your last question, yes, the SIM card will have a UK telephone number.
Edited to add: this page has details on the best value prepaid (PAYG) SIM cards for lots of countries.