Check pump, could be that the impeller has broken or came away from the motor.
When the boiler is on central heating only, place your hand on the DHW outlet, if the pipe gets hot - then it'll be the diverter sticking, with the taps not being open the heat will build up in th pipes and boiler - the boiler will detect it has reached the desired temperature and shut down.
If still no luck - get a heating engineer out to check gas pressures etc.
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