Long post alert!
Here in Guernsey a local company used make a product called Ecostor. They are no longer available after they never achieved popularity and had some performance issues in day to day use.
It was a large unvented cylinder with a six kilowatt immersion, a coil for connecting either an oil boiler or heat pump and a second coil for solar. There was a heat exchanger mounted on the outside of the unit to provide hot water. The cylinder was heated by the solar coil when conditions were right with the immersion as a backup and also as I mentioned connected to a boiler or heat pump.
The water in the cylinder was not what came out of your taps, but rather a thermal store. This stored water was pumped both through the heat exchanger for on demand hot water and through the rads to do the central heating.
The problem was that you more or less had to choose whether you have a warm house or hot water. If you came home from work and put the heating on, good luck getting enough hot water for a family to use in the evening as the heat was lost too quickly to the room heating. Likewise, long showers or big baths would deplete the heat store and your heating would not perform adequately. If used very carefully and in a specific way with timings it would work. Likewise for very small properties like flats, it worked ok.
There was never enough stored heat to do both jobs and the immersions ended up being used most of the time which kind of defeated the purpose of the system. Sorry for the long post but these things were never liked here and are no longer available as far as I know. I've got one here in the workshop as a demo model but I've just finished ripping it out as our apprentices really don't work on them enough to dedicate the space any longer.