SIM card or international phone plan

The newer iPhones (all of them?) use a size called a "nano" SIM that is now widely available, because the newest Androids use the nano size too. Most prepaid SIM cards now are "3-in-1" SIMs where the edges peel off to make the next smallest size, down to the nano size. So there is only one SIM to buy - peel off the edges to make a nano SIM if you have an iPhone.

If you buy a UK SIM, you will have a UK phone number while you have the SIM and won't be able to use your old number anymore (can't make or receive calls on it) until you put the AT&T SIM back in. If you install the Google Hangouts app, you can make calls home to the US for free, even to landlines, on WiFi or with mobile data, so you might be able to use that to check your AT&T voicemail if need be. (By calling your own number and entering the code, I guess, unless AT&T has a voicemail app that would still work without your AT&T SIM.) There are free texting apps as well., but again, you won't be able to receive texts directly via SMS on your old number without your AT&T SIM in place. Not sure how WhatsApp and other texting apps work, but I would try one out before you leave for the UK and use it on WiFi (put your phone in airplane mode first, then turn on WiFi) and see if you can send/receive texts - then you know it will work in the UK, even with your UK SIM's mobile data.

Getting your old SIM OUT is apparently a challenge with an iPhone - make sure you know how to do it ahead of time! Someone at a mobile shop in the UK can probably help, though.

I use WhatsApp. It's free.

Just this morning my time, (PST) but mid day theirs was in contact with friends in Turin and England. Have done video chats as well. Usually its just texting. I have an iPhone 7 and am a Verizon customer. In 2016 my AirBnb host was in China while I was at her house in London. We kept in touch via WhatsApp. Investigate.

How much do you plan to use your phone? Emergencies, or daily data use?

You should switch to T-mobile which has no charge for international roaming. They have an unlimited plan for two lines $60 if you are over 55+ years old.

Richard:

You should switch to T-mobile which has no charge for international roaming.

Not quite. It's still 20 cents/minute for calls. If you need to make an hour of phone calls every day while you travel, it would be cheaper to use Verizon's or AT&T's $10/day plan. T-Mobile does offer free unlimited texting and unlimited (2G speed) data, however.

They have an unlimited plan for two lines $60 if you are over 55+ years old.

Sprint has the same roaming plan that T-Mobile has. But at the moment, Sprint is offering a free year of unlimited service ("BYOD - Bring Your Own Device") for qualified phones You can just buy a qualified phone if you don't have one. I did this a few months ago.

The most convenient approach is using your provider's international plan. No messing with SIM cards, etc. Daily cost will be more but, depending on the duration of your stay in London, could be worth it.

If you go the SIM route the phone does need to be unlocked. Get that done before you leave home.

Phone shops are plentiful in London. Last time I was there I found 4 within a 5-minute walk of my Kensington hotel. I went to the shop that looked least busy where someone swapped the cards, then set up and activated a short pay-as-you-go account for approx $40. Walked out 15 minutes later with a UK number and a working phone. (So remember that anyone back home who may want to call you will need to have that number.)

The catch to this is that you'll need to put your U.S. SIM back into the phone after your return flight arrives.

Thanks to all of you for your thoughtful replies to my questions!
I have considered every option and changed my mind often as to how to deal with communication while in England and France.
Any of your suggestions could work out but I have decided to keep it simple, if not a bit more expensive, and get At&t’s international plan.
I need to make contact with home several times (WhatsApp could work), access google maps and Citymapper as we travel ( understand this can be done off-line) but also my daughter who is traveling with me wants to be able to contact me if we should become separated...we will have two 13 year olds with us so that is a distinct possibility!
The at&t plan charges $10 for a 24 hour period and only when you use it. I anticipate using it for about 6 days of our travel if I plan carefully.
My choice for a longer trip would be a SIM card. Having difficulty downloading WhatsApp but want to check that out.
This forum has been so helpful.
I will try to remember to return the favor and “report” the joys and pitfalls of our journey when we return!