The EF39 was described by Mullard as a variable-mu RF pentode, with sliding screen characteristics, for use as a controlled RF or IF amplifier. The EF9 is electrically identical to the EF39 but is on a Ct8 base. The frequency range of operation would be up to 30 MHz.
The cylindrical anode sits in the centre with the grids extending above and below it.
The screen can be seen between the pinch and the lower mica sheet.
The EF39 is a variable-μ pentode and so one would expect to see the control grid pitch vary along the length with a closer spacing in the centre and a more wider spacing at the ends.
Looking along the control grid no variation in winding pitch can be seen and thus the question arises as to whether this is an EF39.
The classic envelope is 30 mm in diameter and excluding the IO base pins it is 85 mm long.
References: Data-sheet, 1040 & 1043. Type EF39 was first introduced in 1939. See also1939 adverts.