Giffgaff

The Cellular Apple Watch shares the iPhone's phone number, and in order to do that, the carrier has to support the Apple Watch. If EE has not extended that service to giffgaff, then they will not be able to support the Apple Watch. Lots of NVMO, such as giffgaff are not allowed by contract to support the Apple Watch, as the carrier that owns the frequencies do not want to share.

iPhone Cellular Carriers that support the Apple Watch, which models, the radio frequencies each model uses, and the country where they offer service:

https://www.apple.com/watch/cellular

The GPS only version will,the cellular version won't as it's not supported by giffgaff.

Only EE,Vodaphone and o2 support the apple watch.