Right im not having a dig but have you honestly not seen a Classic, a 240 a Solo in the last 20 years, cmon you must have seen a boiler with apilot in that time!
Ive only been doing it 10 years and 75% + of boilers i come accross are pilots
I don't do this commercially! I've installed a couple of central heating systems, but they have been in my own home (more than one house!). Other than that, I've only ever worked with non-pilot-light boilers (eg when a friend/relative has asked me to "have a look" at their boiler)
I genuinely had no idea so many homes still had pilot lights merrily wasting gas all hours of the day and night!
Anyway... I can see the issue with the HW always working with the CH, but that still doesn't explain why when the CH has achieved temperature (room stat has turned off) the boiler still fires up once every 5 minutes for about 15-20 seconds, running the hot water circuit. It's definitely the HW circuit, as if the CH is turned completely off (programmer off) the boiler still does this. The water in the cylinder is absurdley hot (I'd guess well over 80deg) and desperately needs turning down, which is a bit difficult with no cylinder stat. I'd also much rather the boiler did NOT try to keep the HW tank up to temperature all the time, but if it has to run the HW all the time the CH is on, then so be it (and what an irritating and wasteful design that is!)