OG, 4.5 inch rear width was UK standard for fixed wheel and hub gears, up till generally mid 50's. If you have forward facing road rear ends it suggests a Claud Butler rather than a Holdsworthy., who owned the name from the mid 50's. This is well documented, look up Claud Butler and Evelyn Hamilton.
British Hub co and others made gear sided hubs for 4.5 inch, which meant that unfortunates like me had the job of building wheels with the gear side nearly vertical. Fortunately Campagnolo came to my rescue, and on occasion I had to expand the rear width. You would be surprised how soft some frames were.
So eventually 4.75 inches or 120mm prevailed.
If your front fork ends are that tight, being made for a 5/16 axle, either file them out a little, or if using the 9mm front axle QR then file just the tops of the threads where they stick out from the lock nuts.
I have seen early Claud Butler catalogues on line also.
So you might have a CB original or a Holdsworthy.