hello, welcome to the GMB. Regret to say that contrary to some other forums where values are discussed, on the GMB we avoid the subject entirely, since valuations are an area of great personal interpretation, plus the fact that we're not professional appraisers of vintage or antique glass. Sorry to disappoint you.
You don't explain your reasons for wanting one ................ is it just to sharpen your razor blades
or are you a collector of glass?
I've not seen one of these for several years, so no idea if they are particularly collectible at present, but it's possible that if you search the various on line auctions etc. you might find one for sale.
I notice what looks like an error regarding the British Registration No. quoted for the Lillicrap Hone, but I forget which one is correct. In the late Bernard Cavelot's Reply No. 1, he looks to be quoting this as 756250, but in much later references in this thread - and I notice on the pix of your hand written notes that you've posted - this is showing as 756950. I did have one some years back but now gone, so unsure which is right, and I can't find a book which gives the No.
There is a picture of one in Raymond Notley's paperback, but he doesn't give the Reg. No.
If you find one of these things, vastly larger than a Lillicrap example, and I've never seen one here ............ they were apparently marketed for resting the necks of corpses on whilst the deceased was on show in the coffin. When the lid was about to be sealed for the last time, this glass rest was removed, and being glass they were seen as hygienic .............. though not sure if this was a 'tall story' or genuine.