Do you have the missing cooling air cowl for that engine? If so it will have a long series of numbers stamped on it that may help us to identify what carburetor and intake pipe it should have. You have a better chance of getting a good result if you put it back to standard condition.
The plan is to get this thing into as close to it's proper condition as I can. I'm going to contact Cox mowers to see if I can get a bonnet for it. I've no clue what to do about the rear wheels yet, they seem to be off a Morris minor. On the positive side, the cutting gear looks to be largely untouched.