Hi MPT
Well we really do need to know quite a bit more about "the fumes" and how potent / noticeable they were. Just because you become aware of "an unpleasant whiff" does not necessarily mean you have to (or should) take immediate action! Most of us at some stage have experienced the "smelly socks" odour - especially on the first flight of the day. Doesn't mean that you should automatically put on masks. De-icing fluid mistakenly sprayed into or near [run-off] the APU inlet can also result in odours / fumes (unlikely in this case). I am sure that the AAIB will establish at what stage the crew felt that this was actually "an issue that requires action" - and why. As I have said before on this forum: "we weren't there"! However for the purposes of this debate I am assuming that particular point was reached when the crew began to feel unwell and not before. You asked for my reasoning in not immediately levelling / descending / diverting the aircraft - it was thus:
Normally the first course of action in an in-flight emergency is the checklist. In the case here [fumes] this is normally accomplished by "memory items" and then "follow-up actions". In the case of <fumes in the cockpit> then the item that is very, very close to the top of the memory checklist is "don masks & establish communication" (inter pilot initially). Then the rest of the checklist can be followed. One common theme of CRM is "keep the workload as low as practical". By following, at least initially, the original flight path the crew accomplished this. That is the point that many on PPRuNe seem to take issue with. Had there been a loss of pressure that would be very different but, again, that is covered in the "memory items" and I'm sure would have been actioned if required.
Another poster said 'just declare an emergency' and then basically do what you want (my italics). Whilst true this can result in a number of other issues & potential problems. To whit: ATC will need to contact & reroute other aircraft (this was very busy airspace). They are almost certainly also going to contact the subject aircraft with queries such as "confirm ABC is squawking 7700"; and "what is the nature of your emergency" plus the famous "what are your intentions". All of these require crew responses and thought trains that distract from the matter in hand. Yes these comms can indeed be ignored for a while but that further increases workload & ATC anxiety / workload.
The aircraft was flying just fine - albeit with a possible cabin air problem but not a loss of air. The crew, once masked up, were also just fine. Thus the aircraft was in no immediate danger. Follow the checklist which will, almost certainly, end with you having to divert or at least RTB. Just as this, professional, crew did.