The 4045A is a directly heated tetrode the Type designation is of the form that indicates an STC valve. The valve was used by the GPO (UK General Post Office) and was there called the POVT145 and that Type is also on the envelope.
The VT145 was called POVT145 when the CV register was introduced to avoid confusion.
The W421 may also be a Type designation but we have found no details.
The two wire grids seem to have the same pitch. The filament is an oxide coated ribbon - the type normally associated with rectifiers. This tetrode may have been designed as a mixer rather than as a screen grid valve.
The top mica. The wire grids are almost in the same plane.
Slightly enhanced to show the anode construction and the grids close together.
The balloon envelope is 59 mm in diameter and, excluding the B5 base pins, is 146 mm tall.
Reference: Datasheet. Type 4045A was first introduced in 1937.