You don't need to have it done anywhere.
You can go to any carrier store to get a SIM card with a local plan, and insert it into the iPhone yourself. Or have the person helping you out in the cellular carrier store change it out for you.
Cost will depend on the plan you get. Likely pay as you go, and you can add credit to it as you require.
The SIM card itself should be free.
Remove or switch the SIM card in your iPhone or iPad - Apple Support
WIth that said, note
1. Your iPhone must be unlocked to accept a SIM card from a different carrier to the one you currently use.
2. A different sim card means a different local U.K. number, so you won't be getting any calls that are placed to your original number, nor SMS text messages.
3. Depending on the length of your stay, you may be better off with a roaming package from your current cell carrier.