If you can purchase a pre-paid phone card, that would be the better route. Many hotels these days don't charge for local calls but they not only charge for long-distance but often a hefty fee on top of it. Long before I had a cell phone, I used a phone card to avoid these fees.
We have Canadian phones, I use my providers Roaming package when I travel. It includes voice, text and data.
You will also need a cell at the parks for making extra fast passes, etc. I don’t trust park wifi. You could be on it one minute and gone the next.
I also use FaceTime for calls.
Definitely avoid using the in-room phone for international calls. Or domestic long-distance for that matter. I stopped using hotel phones for anything other than calls within the hotel about 20 years ago. The prices for long-distance within the US were insane then, I can't imagine what they are now.
You might want to pose this question on our UK Trip Planning board. I'm sure they'll have lots of good suggestions.