I used my US Uber in Paris without a hitch. I wish Uber offered the ability to include roaming numbers for that purpose or direct passenger communication system. At the airport, the individual had no problem calling a US mobile. In Central Paris, they never called but were always there.
Toggle Mobile and Truphone both offer SIM cards with a US and a UK Mobile number on the same card. You can also get a temporary UK number from Roamer, Hushed, or a ton of other services.