Following people kind enough to answer my questions, and requesting I do a log of the build, here it is.
Be aware - this is not a "how to". I have no idea what I am doing as I have only owned a lathe for a couple of months, and the only engine I have built so far is the simple Elmer's wobbler.
I am using the poppin as a project to learn about machining, so any constructive comments will be welcomed.
First the pictures of where I am now.
The cylinder and cylinder head are finished, and the piston has been made.
My first attempt at lapping the cylinder by hand ended in disaster with the centre becoming a larger diameter that the two ends.
I used an adjustable reamer, taking very light cuts to get back to a cylinder. I then turned the piston to be a tight fit, and brought it down to size using very fine abrasive. It is now a lose but airtight fit. In the picture the cylinder looks quite rough, but I think this is an optical illusion. I will wait to see if the engine runs before trying any lapping again.