If I’ve got a new phone, can I just download the Pingit app again and log in?

No. You'll need to de-register then re-register using your new details. You can do this in the app. Go to 'Settings', choose the details you'd like to change and then follow the on-screen instructions.

If you're changing or upgrading from one iPhone to another, and keeping your phone number, you can restore your registration on the new phone without having to re-register. Just open the app on your old phone, go to 'Settings', select 'Change my device' and follow the on-screen instructions. The first time you run Pingit on a new iPhone, you'll be asked whether you want to restore your registration.