My guess is that it is indeed a hypothetical, "what if we designed to the TSR2 spec with swing wings?" design. Interesting since I'm pretty certain that by the time of Paris 1963, no TSR2 pic had been released, and I'm not sure that even a 3-view had been cleared. Also, it's a pretty good piece of foot-shooting marketing to say that the swing wing is smaller and more efficient than the TSR2 design. Maybe there was a Fort Worth mole in the BAC sales office.
I was as right as I can be in my first post, by which I mean I have found the plane in Tony Buttlers BSP Jet Bombers, the photographs in there appear to be of this very model, but from different angles and the text states how it is 'probably' an early version of the BAC 589 ( not 583) before the intakes were redesigned, they ended up looking similar to those of todays Tornado.
I guess the 'probably' is because at this time BAC were proposing various VG projects numbered in the 580-590 range and it is now impossible to tell exactly which one it is.
You could say that all of these were hypothetical TSR 2 type designs, but they did have project numbers of their own.
In Derek Wood's Project Cancelled he shows a picture of a "Secret" British Aircraft Corporation exhibition from about 1964. The swing -wing Lightning is at the centre of the display, but you can just make out various drawings on a board behind, including a TSR 2 with swing wings. Even more tantalising is a whole row of TSR2-like aircraft desk models with various armament fits shown at the bottom of the board.
Someone with good contacts to the BAe North West heritage chaps at Warton might be able to get more, but I think this is only possible if you worked at BAe or BAC/English Electric. I know there is a brochure on swing wing aircraft based on the display board, but the pictures are according to the person who has it no more detailed than the board drawings. Unfortunately there still seems to be a lot of secrecy about this period, but also much of the stuff was simply junked or ended up in people's studies.
BAe would really be doing themselves a favour if they could rescue some of this material and demonstrate to today's trainees and students what an amazing capacity we had back in the 60s.