I think that the Moth, whilst a stunning aircraft, was simply a creature of it's time and didn't have a huge impact upon the development of British light aviation - if it hadn't been there, something else would.
The Islander (and I speak as somebody who has worked on, and flown them) is another superb aircraft fulfilling an important role for many operators, as well as providing gainful employment for many (including me on occasion). But it's impact on British light aviation design and operations? Negligible.
The AVRO 504 I'd suggest did far more to create a pool of pilots and aviation interest, and to set the trend for future aircraft design, than any other British light aircraft - that gets my vote.
That said, the big aviation event of the 20th century in British light aviation was the Lympne air races, out of which were developed the professional skills of designers at Supermarine, de Havilland, English Electric and Hawkers - who went on to provide the tools to win WW2. It also got the whole country thinking about light aviation as a practical proposition. So, although most people have forgotten about the individual aircraft, those as a class win my vote for most significant British light aircraft.
G