Hello Silverghost,
I've only just joined this forum and your message was the first one I read.
I recently acquired a box of Morris 8 series1 parts and spares for a car which I don't yet own.
In it I found a tax disc holder from the Silverdale Showrooms in Tunbridge Wells.
Like you, I did a quick Google search and drew a blank, but I thought you might be interested to see the disc and I've attached a photo of it for you.
There's probably a record of all the garage businesses operating in Tunbridge Wells from this period, which the local Council may have.
Local postcard collectors (of which there are many - with several local regular postcard fairs held throughout the year) are also a good possible source of information, as many postcards show street scenes, and there may be one out there showing this garage.
I don't have time at the moment to do any further research myself, but if you're still interested I hope my suggestions may be of some help if you want to pursue your search.
All the best to you,
My kind regards,
Howard