OP: get someone to open a hot tap, whilst you are next to the Unvented Cylinder, with your hand on the hot feed pipe coming out of the cylinder. Get them to shout out when they open the tap (or use mobile phones if out of earshot). If you can feel pipe get warm/hot, as soon as you know the tap has been opened, then this will confirm that it is the pipework between you and the outlet that has to be dealt with to shorten the time taken to get the hot water to the tap(s).
If, however, it takes "some time" for you to feel heat at the hot feed pipe, when the tap is opened, then there may be some issue with the top of the cylinder having a pocket of unheated water in it.
Just try this, to confirm that the piperun is the issue.