God knows why you have a vent under the bath mate, anyway just stick a plastic bag over it and tape it up so its air tight, then see if the smell goes. You should get no smell from the waste pipe as previously mentioned that is the whole point of having a trap with water in. Do Not go with your original quote mate that's complete bollox. I could put you a new fucking suite in for less than that lol.
Incy, that black rubber bung is off a low level toilet mate and connects the flush pipe into the back of the pan for flushing.
Kirkstall, Sink waste pipes are a standard 1.5" I can't see Barratts using anything else. Could be down to little /no fall, or build up of waste in the pipe. Not a difficult/dear job to replace if a good plunge out doesn't work. Always take off and flush/clean the trap first though as these tend to block first.
edit* kitchen sink 1.5"
bathroom/cloakroom sink 1.25"