Margaret,
If we trawl back through this problem, from my perspective it comes back to two issues:
From the photographs you have provided, it looks as if the pipework installation is sending a flow to both the flow and return terminals of the indirect hot water tank.
It also appears that the two port valves and possibly the Hive controller have been installed in correctly.
Both of the above give a clear indication that the installer of the system was inept and probably not competent.
To correct this situation you require a reputable plumber, to survey the system and to give you a priced proposal to modify the current installation into a fully working S Plan system.
At that point you can then decide how to proceed to get you system operating properly and (just as importantly) how to recover the additional money you have already spent and will need to spend to rectify the problem.
If the sum is large enough, you should consider giving the original installer one opportunity to correct the installation, thereafter engage a competent plumber and recover your costs through the small claims court.
Which ever route you take, to recover your costs, you need to establish a clear base line ( in the form if a short, but detailed report) now of what is wrong with the installation and how much it will cost to correct. It is equally important to establish a base line to preserve the warranty that you believe you have for the Vailient Boiler. By allowing people (BG) to tinker will a newly installed boiler, you are putting that warranty at risk
It may be that you household insurance policy will provide legal cover to assist in your claim.
I feel sorry for you with British Gas and I think that you should challenge them on the basis that they fitted a part that was not needed. However, if you call people in on an adhoc basis you need to recognise that they are going to charge for their time.
When I first read you post, I interpreted it as a control issue - they are generally a simple fix ( either correcting the wiring or replacing a faulty part). Once you provided photographs of the pipework around the hot water cylinder, it became apparent that the pipework has been installed incorrectly - this is a more expensive fix. It is also harder to interpret system behaviour, when the pipework is fundamentally wrong. I am surprised that you have ever managed to get hot water with the cylinder piped in that way
At the end of the day a system like yours is a very common straight forward installation - it is not complex and is fixable, once the scope of work required to do so is established.
Hopefully the above will help you to establish a clear and successful way forward.