you didn't tell us what your boiler is.
I used to have an old, iron, 15kW boiler, which struggled to heat the house in very cold weather, and you could feel the house cool down when the cylinder (having been refilled with very cold winter water) was being reheated after a bath. The cylinder was balanced down to restrict flow, but the boiler was not powerful enough.
When I had the cavity walls insulated, the heat loss from the house dropped, and it no longer cooled down when reheating the cylinder.
My new boiler is 24kW which has ample power. Now, when the cylinder is beng reheated from cold, all that happens is that the Flow temperature drops for a few minutes, while the (modulating) boiler turns up its fan speed and flame size to build the temperature back up. Within a few minutes it is back up to temperature, and able to start turning its power lower again.
Some people set their programmer so that the HW comes on half an hour before the CH, to reduce contention and simultaneous demand.
Yes, your Cylinder stat might be faulty.
Does it look like this?
http://www.screwfix.com/p/drayton-hts3-cylinder-stat/95630
It runs at mains voltage so you must turn off the power and test for dead before tinkering
What colour is your HW cylinder?