Chances are that its mains. You need mains for your drinking water so the kitchen tap should be mains. Turn off you main stoptap and run the bathroom cold supply. If it is dead, then you bathroom is mains. Bear in mind that your hot could also be mains unvented. This will run for quite a while as the expansion vessel empties with the mains turned off. Another way would be to measure the temperature of the kitchen supply and the bathroom supply. Run both supplies for a couple of minutes and then see if there is a temperature difference. This is not conclusive but a guide. A tank fed supply will be slightly warmer than mains depending on usage. You could also try measuring pressure. Tank fed being lower than mains unless your tank is very high. Good luck.
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