I have owned my Father's bike for the past twenty years. It is a 'Worthy' Holdsworth, bought second-hand in 1945. It's believed to have been built pre-war, and also believed to be from Accles and Pollock tubing, though we're not 100% sure on that. If that is so, it's likely to be a Typhoon from the mid to late 1930s as that was the only model in that tubing at that time.
It has pencil rear stays, surprisingly steep seat and head angles, round-section forks (same number on steerer as seat lug), simple lug work, and has been resprayed in the original maroon with white box lining as per the original, but without transfers, but done back in the 1950s. Chainset is Chater-Lea, bottom bracket is TDC, bars (originally North Road we think) are now Lauterwasser, saddle the original Brooks B17, and Bluemels white guards. Pedals are CL as well. Brakes are GB Hinduminium Coureur, but think they are a later anachronism! Headset is a Brampton with a clip, stem unknown and unbranded light steel chromed.
Serial number is 4913; yes, a 4-digit number on both steerer tube and seat lug; 4913. Can anyone date it from that number, and perhaps more of a challenge, come up with a model when new?
Will post pics shortly.