The Auster J1 Autocrat was a UK production aircraft, the first postwar civil light cabin monoplane aircraft built by Auster Aircraft after WWII. First delivered in December 1945, some 402 Autocrats were subsequently built. There was a mod in 1949 making possible adding a fourth seat to the three-seat aircraft. This was known as the Auster J-1A which you have photographed. Many were re-engined as J/1N Alphas since 1956. There was also an Auster J/1B Aiglet variant. Series production was complete by end of 1947; however some additional were built to special order. A few J/1N Alphas were built from the outset.
The J-1 and J/1A were powered by a 100 Hp Blackburn Cirrus Minor 2 four cylinder air-cooled inverted engine. The J/1B Aiglet differs mainly by having a 130 Hp DeHavilland Gipsy Major I four-cylinder air-cooled inverted engine. The J/1N Alpha also used the 130 Hp Gipsy Major I.
G-CDPG appears to have a different engine cowl/engine? as the mentioned aircraft in their published photographs. All had four exhaust stacks straight out the cowl bottom. A different engine may have been installed in the P. Groves build or rebuild. I don't see the four vertical exhaust stacks or identical production cowl shape on G-CDPG.
I also have production dimensions and performance data if interested.