Completely agree.Then upping it to 24kW might be necessary, btu I can't help think it is more an issue with the Boilermate rather than the boiler output.
We have an estate locally with Suprima 30's and 40's even and they heat the Boilermate's fine. You can heat a cylinder with a 3Kw immersion heater so an 18Kw boiler should be more than ample... it's a matter how "how long" rather than if it's possible at all.
Had a few faulty thermostats on Boilermate's before. Could also be so badly sludged up that it's not actually absorbing the heat properly. But if your hot water goes cold that fast and heating makes it drop as quickly as it does then the store is DEFINITELY not up to temperature; even at a *genuine* 69 degrees it would last longer than that.
Had the Suprima with a faulty PCB causing it to turn off at ridiculously low flow temperatures too but it's been replaced so hopefully can rule that out.
As for the house being cold, that it more likely down to radiators being too small or insulation poor than anything to do with the boiler being undersized.