Hello Katy,
I was interested in your post because I too lived in such a flat for twenty years. I thought you may appreciate a few tips from my experience.
1.) As long as the hot water tank is at least 110 litres, you should have enough water for an evening bath and a bowl of washing up water. I used to put my dishes in soak in the evening, go and have a bath, then come back and rinse the dishes with whatever lukewarm water was left in the tank. Also you have to develop an unusual way of running the bath!
Slowly run about four inches of water into the bath at a comfortable temperature and hop in. Then with the hot tap half on, stir the water with your hands, while controlling the temperature with the cold tap. (Have the water as hot as you can bear it.)
About every ten seconds, you must touch the hot tap to make sure the water has not gone cold, or you will give yourself a lukewarm bath. Obviously the moment it does, you must turn off both taps.
The reason for not having the hot water running fully, is so that the hot and cold water do not get mixed inside the cylinder.
2.) Showering: I presume that there is an instantaneous shower heater fitted. In my area, at least in the summer, the cheap rate continues until 7.30 am. Could you have a shower before this time?
3.) Most flats designed for economy 7 already have a booster switch combined with the cheap rate timer. If yours doesn't you can install an immersion heater timer from B&Q yourself. However, I think I can count the number of times I used the boost on one hand, as I soon got skilled with my bath routine!
4. If yours is a ground floor flat, start the washing machine about 7am. (They use about 90% of the power to heat the water in the first half hour.)
Hope this was helpful. good luck in your flat,
James