As long as Uber is available at your travel destination, the Uber app will work the same as it does at home. Update your mobile phone number in the Uber app. If you are using a different number during your travels, add it to your Uber account.
Can I use my US Uber account in London?
Uber uses the same app worldwide and charges your US credit card. It works via internet service, not phone, just check with T-Mobile to see if they have coverage or a partner in the UK.