The temperature rise through the Willis immersion is dependent on the circulating flow rate due to convection and pipe resistance, if got just right then you can have hot water almost immediately in the top of the cylinder but if circulation too high then the water might only be tepid, if flow rate too low, the immersion stat will keep cutting it out.
I would suggest ensuring gate valve fully open and see/feel immersion outlet temperature and see how long the immersion runs for, you can then throttle the valve to give a suitable temperature rise and almost continuous heating until a full cylinder of hot water. post a photo of yours as these are often installed upside down. You should get ~ 6/8 litres of hot water after 5 minutes or so from a 3kw immersion.