advice needed please

Hi I have purchased my Mg zr 2004 reg recently first day seemed fine then noticed a wet patch on the floor under the car. I notice it only happens when the engine is cold I fill thevwater up and by the end of the day its empty. The garage believes I need a new water pump but there's 2 sorts and the garage cant find the engine number so unsure which one I need please help me so confused and don't know what to to

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