I have a Baxi 80Eco myself and, in my experience the most common cause of this problem is (a) a ruptured diaphram in the DHW (Domestic Hot Water) pressure sensor or (b) more commonly, the plunger which is activated by that diaphram suffers corrossion and sticks in either the open or closed position. This pressure sensor is used to control the diverter valve which provides DHW on demand and has priority over the central heating. The plunger operates a microswitch which in turn (via electrical connections) operates the diverter valve. If this plunger sticks in the open position, the central heating will not work, the pump will run continuously, the extractor fan will cut in regularly and the gas will ignite regularly and then extinguish. If the plunger sticks in the closed position, you will have no DHW at all. However, if you have a puncture or rupture in the diaphram which operates this plunger, then you will need to turn on the hot tap fully in order to build up and maintain enough pressure for the plunger to remain in the open position. You may even notice an extremely small water leak or limescale build-up around the plunger and diaphram housing.
This might not be the cause of your problem, but I hope the information is helpful.
Tony
November 2006