The HL13 was made by Mullard in two versions. The Ct8 based type HL13 and the B7 base option the HL13C. Although not in the literature Mullard also made a B5 based HL13. Mullard describe this valve as an indirectly heated medium impedance triode for use in DC/AC mains receivers.
Hivac also made an HL13 but only in B7 base and the characteristics differ slightly from the Mullard. The essential difference is that the Mullard version has a 13 Volt 200 mA heater, whereas the Hivac uses a 13 Volt 300 mA heater.
The use for the valve would have been as an RF amplifier in radio receivers.
The reverse is plain gold coloured zinc paint.
Looking into the top reveals the top mica but little else.
The classic envelope is 40 mm in diameter and, excluding the Ct8 base pins, is 101 mm tall.
References: Data-sheet & 1043. Type HL13 was first introduced in 1934. See also1934 adverts.