As far as I can make out, there are 3 x 777s currently based at LGW with a First cabin, G-VIIV and VIIW and VIIY. There are 13 777s based there in all. The three I mentioned appear to be focused on ensuring BGI has First aircraft, plus there have been some weather related diversions in the Caribbean recently too. Essentialy not enough aircraft, and I would guess BDA isn't running full at the moment.