I don’t want to keep causing confusion here, but that headset you linked to on Chain Reaction looks very much like an integrated headset, while it looks like (from your picture and the info available) the bike needs a semi-integrated design.
Semi-integrated and internal are the same thing – integrated isn’t.
Integrated headsets, like the one linked above, have the bearings sat directly against the frame, with no cups pressed into the headtube.
From the chain reaction page:
• TH Brand 36/45 degree micro angular contact bearings (blue seal) fit directly into a 45mm OD headtube
Semi integrated/internal headsets use cups like a traditional headset, but they sit flush in the headtube to give a low stack height.
Headsets are a right ballache. I think there are approximately one million combination of standards.