On Mon, 19 Jan 2015 09:18:43 -0800 (PST), wrote:

A separate question is whether he even has the right to discharge into
your back garden at all.

Aye, check the orginal planning permission for his extension and the
plans submitted. If the extraction vent is not on the plans it's
their problem.

You'd probably be within your rights to just ignore it, block it up
and build. But that really is not the way to go as it's likely to
lead to litigation and the only winners there will be the lawyers.
And you don't want to end up in a petty neighbour dispute.

One can't help wondering why you've got as far as building before
noticing the vent. Who drew up your plans? No site visits by
planners, architects, builders quoting, etc...

--
Cheers
Dave.