Your problem sounds very much like you have a faulty thermostat that has a too big a differential between cut in and cut out temperatures. This problem is easy to identify as it happens when the water is not used over night and the water heater comes up to temperature then shuts off the burner and when it drops below say 11 degrees C it should then activate it again to ensure the water is always hot. When you turn on the tap in the morning the first run of hot water will be tepid then the flow acts upon the thermostat and starts the heating session off again so the water gets up to full temp for the rest of the day and then the problem reappears again the next morning.
Get a licenced Gasfitter to replace it for you as any gas work done by persons who should not be doing it can have very dangerous outcomes.
Selgas Services Ltd
Craftsman Gasfitters, Plumbers, Electrical Service Technicians