In most cases when the CH is good but the DHW fails to come on it is the diverter valve diaphragm which has perforated. Replacement is straightforward, without need to drain the CH system.
Have an assistant operate a local HW tap while you watch the diverter valve's operating pin. If it doesn't move swiftly over, or it only travels a couple of mm this is a good indication the diaphragm is shot.
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