The CV4056 is a special quality 6CH6 fitted with flying leads. The B9A based version is the CV4055. The design purpose is as a video output valve. The prototypes were the CV2127 and the 6CH6.
The KB/AD identifies this valve as being made to specification K1001 or K1006, the B denotes qualification by a UK authority and the AD identifies the maker as Brimar - Thorn-AEI , Rochester.
The Two wire grids pass flat across the cathode. The control grid is a much finer pitch than the screen grid. Both can be seen in this image.
One side of the anode.
The thin glass tube envelope is 20 mm in diameter, and excluding the B9A flying leads, is 58 mm tall.
References: Data-sheet, 1040 & 3002. Type CV4056 was first introduced in 1956. See also1956 adverts.