I always buy a sim card when traveling abroad, but never did it when traveling to 3 different countries. I have no need for making calls (international or local) or sending texts, just data.

Is there any SIM card that I could buy in London and would work in other cities in Belgium and in Paris?

If you have a recent iPad with wifi + cellular that has an Apple SIM you can sign up for an EE plan in the UK without even buying a separate SIM, or sign up for GigSky which works internationally.

I've used my Apple SIM with EE, but haven't yet tried GigSky. You can buy a GigSky SIM for other devices through Amazon for as little as $20:
https://www.amazon.com/gp/offer-list...&condition=new

I have a Galaxy 5 and we just went to the Verizon store near us and for a very cheap rate (I think it was $5/month) we were able to use that plan without purchasing a SIM card.

I'm not from the US, so Verizon isn't an option... And my carrier charges way more than that to use my phone abroad.

The sim card is for my iphone so I think the 1st option wouldn't work either.

Take a look at 3...the smallest of the major British mobile operators (three.co.uk I think but you can google them). They, at first glance, have plans that allow you to use data for 1p/mb in many European countries and even the USA although for only a limited time but it should suffice.

xyz123, thanks! I'll look them up.