Extractor fan in chimney breast?

[Toastandjam]

Solid Stone Wall Cottage here.

I'd like to place our cooker against the chimney breast and have the extractor fan above it on the chimney breast wall.
I've been told that you can't run a flue from the hood vertically up the chimney because the moisture would run back down, not to mention build up on fats etc....lots of reasons really.
So the only option I can think of would be to take the flue horizontally from the hood, through the chimney and out through a vent in the external wall.
However, I was told by a sparkie that Bulilding Regs wouldn't accept this work around.

Is that right?
What's everyone else done? I see cookers placed against chimmey breasts all the time.....

Thanks.