communication in europe

It's economical to purchase sim cards at Heathrow (or elsewhere) but it's not economical to purchase phones. Do you require a smartphone or simply a phone to make and receive calls? A basic no frills phone won't be too expensive but would be more expensive than unlocking your current phones and buying a sim card in the UK.

What plan are you on in the US? Some offer reasonable international calling plus data plans. The advantage of these is you keep your same phone number. (One disadvantage is you may get unwanted calls or calls at odd hours. We turn off our phones at night and at all times we only answer the numbers we recognize.)

Check out the Travel Tips: Phones & Technology section of this website simplest thing is to get phones unlocked and getting SIM cards in England.

Would it be better to have our state-side phones unlocked (one is an Iphone and one is android) or just to purchase phones and SIM cards over there?

These are not alternatives. You need an unlocked phone AND a new SIM. The options are:

1) Use your existing phone with your existing provider. You will need to contact your provider to find out how much it will cost. People ringing you call your standard number and pay standard charges. You pay for transferring the call from your country to where you are (so-called "roaming charges"). When you make a call you pay extra to send that call to your home country.

2) If you have an unlocked phone which is compatible with the European "GSM" system. (it MUST be unlocked AND support GSM), buy a SIM card when you arrive, and put it in the phone. You will now have a new phone number from the country you bought the SIM card in. People phoning you will have to be informed of your new (UK) phone number and ring that.
This will work in all European countries, but it will keep its UK number. There will not be any surcharges for calling within EU countries.

3) Buy a new phone AND a SIM card. Do this if you haven't got a compatible unlocked phone to use. Otherwise as above.

Buying at Heathrow is likely to be more expensive than a shop outside the airport.

See this recent thread where we have been talking about it in detail:

https://community.ricksteves.com/travel-forum/tech-tips/complicated-phone-needs-abroad

If your phones are Verizon phones, they are already unlocked most likely. Verizon doesn't lock its phones anymore. AT&T does lock their phones, but if they are paid off you can unlock them for free on AT&T's website:

https://www.att.com/deviceunlock/#/

If you have T-Mobile or Sprint, you shouldn't have to unlock - just use your existing service as they both have a good international roaming plan (free roaming data, 20 cents/minute calls).

It would help to know which provider you're using in the U.S.?

Given the length of your trip, the easiest solution would be to ensure your phones are unlocked and buy SIM cards when you arrive in the U.K. I'd suggest waiting until you get into London and visit a Carphone Warehouse as they sell cards from all the networks and can recommend the best plan for your needs and the countries you'll be visiting. The sales staff should be able to help you set it up.

You'll likely be using a prepaid plan, which means the card will have to be topped-up from time-to-time. Be sure you're clear on the method of topping up once you've left the U.K. Also give some thought on whether you'll need data, or just basic services like calls and texts.

Of course, one disadvantage with using a European SIM is that your number will change, so anyone from home that needs to contact you will need to dial an international long distance call. Will you also be travelling with a Laptop or Tablet to check E-mails via WiFi?

FWIW, I've just been using roaming with my home network on recent trips, as it works well and is the easiest and most convenient method (but not the cheapest, usually about $100).