This very same car came up for discussion last year.
What brand of cobra replica do I have?
The only US manufactured Cobra replica that used a small diameter, triangulated spaceframe chassis was Bennett. The suspension and all chassis details didn't quite match up, but the basic frame design and the extra wide wheels and tires fitted inside the wheelwells led me to speculate that it may have been a semi-home built job using a basic Bennett frame. Also - Bennett made at least 2 generations of chassis designs, moving to the tubular spaceframe in gen 2.
I'm pretty sure the body is from Bennett though, because of a number of matching details. Mainly, the area around the engine compartment opening is unique and identical and there is no rear fender cutout for the fuel filler. Compare to pics in the BAT ad.
Conclusion - this is a Bennett based replica in some form or another.
Bennett chassis illustration:
