The idea is a very attractive one and it has been done, David Gingery published a book about doing just that. I believe the book is still in print and available in the UK. If you do a search on his name you will find a number of sources.
However, IMHO it is not worth the effort, after spending a lot of time building one most people end up with a lathe that is not very precise. Better to spend all that time learning on a "store bought" lathe by actually using it. I believe in the end you will be much more satisfied. Either way good luck with your quest.