Is it a Balanced flue ? if so it should have the manufacturers Flue terminal kit fitted
If it is a Conventional Chimney it should be lined and have a "Chinamans Hat" type Cowl to stop rainwater.
You don't say how old the boiler is but i'm guessing that it is not new, if it has worked OK for a year or so it probably needs a good Service by an OFTEC Engineer who will be able to clean and then set the burner to give clean & efficient combustion
www.oftec.org will assist in finding a r3egistered technician near to you
www.elanar.co.uk, May 2009