Designed specifically for use with Economy 7 off-peak rate overnight electricity, Economy 7 Quartz is the standard by which all other water heating controls are judged, and is the all-time best seller in water heating controls.
www.securemeters.com
has both the User and Installation Manuals for you to read ... the E7 times should be preset correctly but who knows? (ON time between 4.5 and 7 hours and between 23:30pm 09:00 and affects the bottom element only).
Boost only does the top element.
It may be worth checking when the timer is set to go on/off as I can't tell by the photos.
The Gledhill is 120 litre capacity so a BDIR20 900mm high x 450mm diameter. The bath must be bigger than some modern ones if there's not enough hot, perhaps?
The lower immersion heater element must be working...
No hot water otherwise as you haven't used the top (boost one before).
As Harry suggests, under the black covers of each of the elements (!!! isolate the mains before opening !!!) will be a thermostat that could be set a tad higher for hotter water (which then presents an increased scalding risk) that might do a tad better at filling a bath?
It would need around 2 hours of on, to fully heat the cylinder.
That's probably around the minimum time and it could need around 30 minutes of that time (1.5kWh) to make up a days' worth of heat loss from the cylinder... excluding losses from all that uninsulated pipework. The Gledhill is a well insulated beast though!
A moot point though as it is supposed to have been on for a minimum of 4.5 hours (the thermostat will switch off when satisfied the water inside is at the right temperature some time sooner).
OP should really be asking the HA to supply this shower-booster or electric shower? {I'd say the same if a private Landlord rental.}
I'm also slightly surprised the Bath filler/shower isn't a thermostatic one (as current Building Regs require) if in a HA letting?
OP also needs to ensure they have a peak/off peak rate metering tariff to take advantage of heating the water overnight...