That is a Gibson ES-335. In most of the video, the finish looks like either “walnut” or “wine red”. But that might just be the lighting and video quality. In a couple closeups, the finish looks closer to the more common “cherry red” finish.
Near the end of A Punch Up at a Wedding, we can see a small sticker on the instrument’s pickguard. The sticker seems to read “Gibson”.
The guitar has a selector switch on the lower horn, so it’s definitely not Ed’s vintage 1964 ES-335, which lacks the switch.
Jonny playing the ES-335 during A Punch Up at a Wedding in Montreal.
At the Musique Plus show, Jonny used the guitar for I Might Be Wrong, Sail to the Moon, There There, Go To Sleep, and A Punch Up at a Wedding. Thom played the guitar too, strumming it during I Will. In fact, it was the only electric guitar either of them played at the show. They clearly wanted to bring less gear on that day: for most of the 2003 “acoustic” tour, Thom and Jonny both played acoustic on I Might Be Wrong, but this time Jonny stuck with the electric.
We’ve only seen Jonny use that guitar for the Musique Plus show. It’s not even in the long list of instruments that Jonny used for an Electric Counterpoint backing track (he re-records all the guitar parts for each performance to keep them unique).
So most likely, the guitar was borrowed or rented for that show. This perhaps explains the sticker: Musique Plus probably had extra guitars for guests to play, and maybe the sticker made the guitar easier for staff to recognize.
But unless we see Jonny or another member of Radiohead with it, we’ll never know for sure.