Plumbing – What could cause the hot water to run out quickly… but only in the bath/shower

My (London, UK) apartment building's hot water comes from a district heating system and is delivered to my apartment via a "Heat Interface Unit" within the property, owned and maintained by the energy company. Water from the main and the HIU is piped to the separate rooms in the property from a central closet.

While running a bath a couple of months ago, I noticed the hot water run out before the bath was even half full (previously the hot water supply seemed endless). A few weeks ago, I replaced a split shower hose in the same bathroom with one which happened to allow a higher flow rate. The next morning with the shower turned up to full flow I noticed it start to get cold after only a couple of minutes. Prior to this the shower would run seemingly endlessly with no loss of temperature.

I rang the energy company and they asked me to try my heating, which uses hot water from the same system. They said the HIU would only be at fault if the heating was also not working correctly – I tried it and it was fine, with all four of my radiators heating up quickly (worth noting that I normally never use the heating as the building's ambient temperature is high). I ran hot water in the bathroom sink and in the kitchen, and these seemed fine as well. Their policy is to only send an engineer if the fault can be demonstrated to be with the HIU, so I've sat on the issue for a bit.

On subsequent showers I found that if I kept the flow turned low – around 60%, the water would stay warm for the duration of my shower.

This evening I tried to run a bath and the same thing happened – the hot water ran cold (24ºC) after only a short time. The kitchen tap ran hot (46ºC) without issue. In the bathroom, I found that if I switched the bath tap off for a minute, then back on, it would run very hot very briefly, then back to cold. The tap over the sink seems unaffected – running hot for as long as I care to test. If I run the bath tap at the same time, both go cold. However if I switch off the bath tap, the sink will return to hot, but not the other way around. I note that the flow through the bath tap is much higher than the sink, in case this is relevant.

I am struggling to come up with a mental model of the plumbing that explains why the hot water supply (seemingly to these two appliances only) is being affected in this way, given all the hot water pipes seem to branch from the same point in the system. Can you think of anything that could cause this; is there any sensible further investigation I should do; could the HIU be at fault, or am I best off calling a plumber?

I attach summary photos of the submarine-control-panel-like HIU and the point of distribution of the water pipes. Also a floorplan of the apartment with the HIU closet marked with a red dot.

Thanks for your time and please let me know if I can clarify any of the above points!

Edited to clarify detail around the bathroom sink tap after further experimentation today.