Not at all. It was built by the successor of British Marine Aircraft, the company was re-named after Henry Folland when the company was reorganised in 1937. Folland Aircraft took over BMA's site at Hamble.The Gnat was desigmed by W.Petter who had designed the Lysander, Canberra and Lightning. The Folland Midge prototype lightweight jet fighter which first flew in August 1954. It was followed by the Folland Gnat advanced trainer in 1955. Both were built at Hamble until the 1960s.
Folland Aircraft was one of the many victims of the post war rationalisation of the aircraft industry eventually becoming part of BAe Systems. I'd have to check with my brother in law but I think that the company still uses the Hamble site.
The Red Arrows flew the Gnat and you can't get a better British endorsement than that
Cheers
Steve
Edit. S,i I think that the Gnat may even have been built under licence in India, like the Hunter.
The Gnat was the first Red Arrows' aircraft, though various jets had been flown by various RAF display teams previously.