Sadly that seems to about sum up this forum at times - there's a good number of knowledgable and helpful people, but there are also some "less helpful" people who seem to like making themselves heard.
My personal opinion is that combi boilers have no place in a situation like you describe* - there's already a hot water cylinder, so the "space saving" is not required. The hot water flow rate is a fraction of what you can get from a cylinder**, they leave you without hot water as well as heating when (not if) they break down, and the combi function adds complication to the device so they break down more often.
* Developers love them because they can fit more shoeboxes into a given size of development - but then they don't care about what's good for the users who end up living in them.
** With your cylinder, the ONLY restriction in flow rate is the size/length of the pipework. With a combi the flow rate is limited by the capacity of the boiler to heat the water AS YOU USE IT. The combi can supply this lower rate effectively for as long as you want, while the hot water cylinder will run out - but that's only an issue if you use more water than the cylinder is sized for without a suitable recovery time in between (the classic issue being a family taking baths one after another with a too-small tank).
Do the sums, it takes 4.2kW to heat 1 kg of water through 1˚C in 1 second. For a cold mains and a decent water temperature, the flow rate from a combi is somewhat restricted - and that's allowing for them being (typically) grossly oversized for the heating load.
If your parents do decide to look at thermal solar panels, then it's quite possible you may have a thermal store or heat bank recommended. Mention them here and you'll find a certain amount of frothing at the mouth from some people who will tell you that they are the worst thing ever created. Mostly these are the same people trying to claim that combi boilers are the best thing since sliced bread. A thermal store is an great way to combine multiple heat sources - such as a range/Aga/whatever and solar, with gas boiler as back up and top up. It'll run both the hot water and heating from any of the sources while separating the often conflicting requirements (eg you can run a fully TRV heating system without worrying about minimum flow rates through the boiler). The main downside is that they cost "somewhat more" than a cheap hot water cylinder, the second downside is that you'll need to choose you plumber carefully if you don't like explaining to them all that no it's not a load of rubbish and it doesn't want ripping out to be replaced with a combi
Lastly, a combi isn't necessarily more efficient that a how water cylinder. If they don't have a pre-heat or keep warm facility then you have a wait before you get hot water - and during that time you waste water and energy waiting for the hot tap to run hot. If the boiler does have some form of keep warm facility, then that has losses as well - it's only one datapoint, but when I compared the standing losses between the thermal store in my flat and the combi boiler in the house with it's keep warm function on, the thermal store had slightly lower standing losses.
However, a new A-rated boiler in a properly designed system should be more efficient that an old one.
