Ah well, time to get in touch with the landlady. And in the meantime... well, the shower has its own heater, the washing machine only uses cold water, and I can always use the kettle to heat water for washing up. Really, an instantaneous hot water heater would probably be more useful and efficient than a hot water cylinder.
In other news, it turns out that Lakeland no longer stock those solar lights nor do they have replacement parts, which is a shame. But they have offered a refund which I did not expect at all. Ten brownie points to Lakeland for that!