The C1 is a barretter, that is a series resistance to stabilise current flow. The barretter characteristic comes from the use of iron wire. The attached data sheet has a good explanation of the barretter and its function.
The C1C is electrically the same as the C1 but fitted onto a B4 base cap.
The introduction of AC mains in the UK was a gradual affair with some areas opting for DC supplies and remote areas having no mains electricity. DC mains supplies could not be transformed to other voltages with transformers and so for radio receivers the 'Universal' sets were introduced. The HT came straight of the mains and the valve heaters were series connected with a dropping resistor also across the mains. Mains voltages can fluctuate and thus so will heater current and cathode temperature. The barretter would keep the current constant over a small range of changing voltages. When DC mains were replaced with AC the need for universal valves reduced. However the series heater chain came back into fashion with the post war television receiver.
By enhancing the photograph the etched wording on the dome becomes clearer showing the made in England wording. The other C1 shown was made by Philips in Holland.
The fine wire showing the coiled structure and the method of support by clamping the wire to metal spokes embedded into the central glass rod.
This image is from the barretter from the Philips box referenced above. This style of construction was used by Philips from the 1920s onwards.
The wide glass tube envelope is 38 mm in diameter, and excluding the Ct8 base pins is 115 mm tall.
Reference: Data-sheet Type C1 was first introduced in 1934. See also1934 adverts.