Firstly, I totally agree with what you imply: The boiler size is not the issue at all. I am unclear on just exactly what the "setup" is but is it a "vented" system - is there a header tank on the boiler circuit ? This would be a smallish tank filled through a float valve, positioned somewhere above every part of the system, like in an attic or elsewhere up close to the ceiling - it will be entirely separate from a tank to fill up the hot water tank (which would be of significant size).
Also, it is not clear to me what level/type of controls you have but it sounds like, as in 99% of British homes, there is a timing/rationing/quota device involved. Can I suggest that you set that device to continuous operation (all day and all night) and see what happens, how the system behaves ? Once that is clear add a description to your post and then more informed/detailed advice should become available.