Nice engineIt's the engine Villiers made for ATCO lawnmowers. About 98cc if I remember correctly. I own one too and I wish I had more just like it.
https://www.youtube.com/watch?v=CKrJJulXw_M
Any ideas where one could find a carb and exhaust for this little baby.
Sorry I am no help there, but you have a 1973-1977 Harley-Davidson Sportster front hub supporting it.
Have you tried smokstak dot com for the carb or anyone familiar with Villiars?
E.bay Uk is the best place to hunt for a carb. Some British Seagull outboards used the same Villiers carb so that can be a useful direction to hunt in as well. The exhaust systems are very basic and wouldn't be at all difficult to fabricate. Buying the genuine article NOS would be expensive and old second hand ones are usually clogged up with oily carbon residue and aren't worth buying.