The problem I have is that the temperature of the water goes from
either freezing cold to scalding hot in a cycle of probably 30-50
seconds. No amount of adjustment of the control helps me. any ideas
anyone?

The Mira 415 is a pressure balancing shower mixer without thermostatic
control. Therefore, the problem is likely to be either varying pressure on
one of the supplies not compensated for by the pressure balancing valve. Or,
more likely, there is an issue with the boiler not regulating temperature
properly.

Also what would I need to keep the pressure/temperature constant if
someone flushed the toilet or used another tap?

You are unlikely to improve the performance in this regard without extremely
disruptive and expensive work. However, you can mitigate the effect by
turning down isolator valves to the minimum acceptable flow for each outlet.
There is no need for the toilet to fill in 20 seconds, or a basin to blast
out the water. If you turn down these isolators, then the effect of using
the tap/toilet will be reduced.

Christian.