Excuse me butting in - but it seems to me that there has been some confusion and 'cross-purposes' regarding the "side Entry" mentioned by JackK in post no.8. Your HW cylinder doesn't have and doesn't need a flange fitted on the side (an Essex Flange) - you already have a flange fitted at the top...
Actually, there would be no need to dismantle the cistern to replace the diaphragm - the Dudley flush valve separates into two parts for exactly that purpose.
I've had a quick look through the manual, and can't find any reference to a quick rinse-only programme. Strangely, the manual does state (under 'Hints & Tips') "Do not pre-rinse dishes by hand". Perhaps have a read of the manual yourself?
Looks like a Shock Arrestor - like this: https://www.bes.co.uk/mini-expansion-vessel-shock-arrestor-11355?ref=gs&photo=true&gclid=EAIaIQobChMI_enO56-K3AIVCL7tCh3mWggpEAQYAiABEgIXAPD_BwE
Fitted to help with Water Hammer.
In your picture, the two 22mm pipes on the right hand side are labelled "SH" and "SC". Shower hot and shower cold, perhaps? Each has an isolator, so try turning those off to confirm that they do in fact supply your shower.
Looks like an AquaLisa 609, spares for which can be ordered from Shower Doctor. Here's a link to that model: http://www.showerdoc.com/aqualisa-aquavalve-609-thermostatic-and-409-manual-shower-spares
If memory serves me correctly, you need to pry out the sticky red & blue Aqualisa badge...
Thank you for replies so far. However, nobody has yet answered the main question - which is whether or not the gaffer-taped flue connection can be properly corrected.
Money is tight when moving house, and if my RGI, when servicing/inspecting the boiler - classed it as 'At Risk' or even...
I'm looking to move house shortly, and am viewing various properties. Among features I am looking at is the make and model of boiler installed, to try and get an idea of reliability and servicing costs in the future.
My current favourite house has this boiler installed in the garage