I'm going to guess that it is white. So it is an unvented cylinder.
I'm going to guess that it has 250 litres capacity.
So the boiler should be able to heat it in about an hour.
An unvented cylinder can deliver a very powerful shower. I'm going to guess that you have Drencher showers delivering 20 litres per minute.
Three people having five-minute showers would use 300 litres of water.
Some hot, some cold, but (on my guesses) enough to use all the hot water in the cylinder.
This can be addressed by having the boiler timer set go "HW on" at least half an hour before the first shower, staying on throughout the showering period, and for half an hour afterwards.
As regards economy, white cylinders are very well insulated. Once the water has been heated, it stays hot until it is used (or for several days, whichever is the shorter). Leaving the boiler on for two hours will not use twice as much energy as leaving it on for one hour, it just uses whatever is required to bring the water to the temperature on the thermostat.
A white cylinder containing 250 litres of water is more than enough for a day of washing up, so will not need topping up again until shower time comes round again.
(There is however an advantage to turning off the HW outside the bathing and showering period, otherwise the boiler may start up for a few minutes every time you run a hot tap to fill the sink or something. This is uneconomical because every time the boiler starts up it has to heat itself and the pipes, and short runs are wasteful. This is why an hour or two twice a day, leaving the cylinder with sufficient hot water for minor incidentals, is cheaper.)