It's about impossible to say exactly who made your pistol but the size and shape of the grip indicates it was most likely made sometime between 1795 and 1820. That seems to be the time period the "bag grip" your guns stock has was popular in England.
If you haven't figured it out, it was called a bag grip because it is shaped like a small, full bag.
The English pistols in this time period that are shown in the book,
Pistols of the World , Claude Blair, ©1968, THE VIKING PRESS, N.Y. shows several guns similar to yours, #280, 281, 282, 283, 360, 362, 363. (The 300 series are percussion guns).
Finding a lock that would fit your pistol without modifying it or the lock mortise would be very difficult.
Modern locks that might be made to work include the "Chambers, Small Queen Anne pistol flint lock", "Chambers Siler small flint lock", L&R Durs Egg flint lock" and the "L&R John Bailes of London (small Manton)" lock.
All of these locks have different shapes but if you are interested in trying to figure out if one of them would work, here is a suggestion.
Go to Track of the Wolf's web site and order one of their catalogs. You will find a link to this here.
https://www.trackofthewolf.com/Categories/PartDetail.aspx/303/1/CATALOG-18
The catalog costs $10 + postage and it will show you each lock in exact, full size photos.
You can then trace the shape of your locks mortise on a sheet of paper by placing the paper against the stock and rubbing around the mortise with a lead pencil. The pencil will leave a darker line where the edge of the mortise meets the paper.
Once done you can cut out the shape and compare it to the photos in the book.
If there is an area where the stock wood would have a gap between it and the lock photo, that lock can't be used. By gap I mean, if the cutout is larger than the photo in some area, that lock would leave a gaping gap if it was put into your pistols stock.
If the lock photo is larger than your cutout either the lock can be filed down (a little) or the mortise in the wood can be enlarged (a little).
Let us know if you bought the book and what you find.