What is the arrangement of the HW pipes from your HW cylinder to the upstairs? If the pipe comes off the top of the cylinder and then up to the first floor it is highly likely you are getting gravity circulation - the same as is used for many back boilers and even oil boilers (don't know about gas) to heat the tank upstairs.
Yes there is a pipe from the top of the cylinder which is normally warm to the touch.
One way you can possibly combat that is for the pipe leaving the tank to go down to level with the bottom of the tank before going back up, that way the lower density hot water cannot rise that easily to your upstairs but the pump would be unaffected.
This sounds interesting and should be fairly simple to implement. Would this cause any other issues?
Not that I am aware of, but I am not a plumber or heating expert. I believe the appraoch I have suggested has been mentioned on this forum in the past as a way of reducing losses (I think that is where I first learned of it).
You say you have a pump switched on for an hour in the morning which sounds like a lot depending on the pump performance, do you have a themostat on the return to turn the pump off when the returning water is hot enough - that could save you a significant amount of energy.
Yes the pump is on for an hour but it can be changed with a timer, we set it for an hour because it normally when we are having showers. I don't think there is a thermostat on the return. If I installed a thermostat what temperature should I set it to I assume it would always be slightly cooler that the temperature of the tank hot water? The pump is connected to a pipe nearer the middle of the tank, I assume that it pumps cooler water into the tank and that the hot water goes out of the pipe at the top.
I think the temperature for the return (assuming it is just for circulating DHW) will need to be set by trail and error, but there are some "obvious" considerations. How hot do you need the water at the taps, if only at 38C for hand washing or 42C for a shower then there is not point in returning water at that temperature to the tank. do the basins, baths, showers have thermostatic mixing valves as there is no point in circulating hot water that more than that needed at the outlets. Putting the thermostat at the return near the tank is probably easier, but putting it further back along the pipe would be more beneficial, such as just before the last outlet (assuming it is used - if not the one before that) as there is no point in just heating the pipe.
Make sure you HW pipe is fully insulated including any drops from it. Is it copper or plastic as copper can also drain away heat if it is in contact with other things that can act as heat sinks.
Whether you are better off with seperate feeds to each outlet, or with a larger pipe with separate drops does depend on a number of issues.