Boiler/water pressure issues

ThisIsWeird

KaratePigeon said:

Sorry for the late reply. I was hoping the plumber who came last week would have got back to me with a quote for some options but nothing yet 🙁 I have been bombarded with calls from octopus to see if I want to buy a heat pump though 🤣

That pipe that comes from the top of the cylinder just goes horizontally into a T, the upwards pipe just disappears into the ceiling, and downwards through the floor. 

The shower with just the hot turned on makes a gentle spray. 

The pump under the bath (as I bought it last year) is this one,  as a plumber recommended it 🙄 https://www.screwfix.com/p/salamander-pumps-ct55-xtra-regenerative-single-shower-pump-1-5bar/13775?gclsrc=aw.ds&gad_source=1&gclid=Cj0KCQiA_NC9BhCkARIsABSnSTZJQcgdqpLVjKnL7eekZ3v4ehOoNZz7SGWGGmBiFPhauRJR6-2-vEUaAhgoEALw_wcB it's just connected to the hot water pipe

Ok. The outlet from the hot cylinder isn't ideal, as the 'sucking' pump will be drawing on the water in that pipe that goes through the ceiling, as much as it'll be drawing from the cylinder itself.
If anything limits the cold supply to the cylinder, then the pump will definitely be drawing heavily on that vertical vent pipe, quite possibly to the point where it actually draws air into the pipework = non-functioning pump (and the symptoms you described).
(The pump, by the way, looks very suitable, tho' it does have a disappointing number of negative reviews for faults).
Solution? Very likely a Surrey flange will sort this, and it's an easy and affordable fix.
With luck your pump is still actually working, so can resume good service once this has been done.
Do you have access to it? Can you see how it's been electrically disconnected? Could you reconnect it?
If so, please try this; 
1) see the long vertical pipe to the right of the cylinder, which connects to it near its bottom? That's the cold water supply from the CWS tank to the cylinder. Ok, see the red wheeled valve on it? Cool, give that a clockwise turn to check it can be moved freely. If it can, then open it fully by turning it anti-clockwise until it stops, and then close it a half turn (Ie, you are checking that it is fully open. The 'close-half-turn' bit won't affect the flow, but will help the valve to not seize.)
2) connect the power to the pump.
3) open the hot bath tap only, and just at a trickle. 
4) slowly open the hot tap further until hopefully the pump fires up - don't open the tap any more than this. Let it run for 30 seconds - is it all ok? Pumping well (tho' obviously limited by how little the tap is open)?
5) open the tap further until it's near full. How does it behave? Pumping well? Or getting noisy? Any spluttering? If so, turn it right down again, to the min flow that still has the pump running - does it quieten down, and does the spluttering stop?
Please try that, and report back.
From what you say about the gentle hot flow from the shower, I don't think taking a dedicated cold supply from the CWS is a solution - your 'head' just isn't high enough to give a good shower; the mixer would need swapping for a true low-pressure type for a start (0.1 to 0.2 bar).
See what your plumbers suggest, but don't commit to a fix until they fully explain it, and you understand.