The building regs, including part F, only applies to new builds or substantial alterations. I wouldn't think a kitchen revamp would be defined as substantial or that building control are involved in this. However, assuming that you won't have to comply, part F does provide some useful information on what you might wish to achieve.
I believe that the problem you are trying to overcome is excessive heat, and possibly condensation, build up in a kitchen with no natural ventilation and the obvious solution is a good extractor hood over the cooker range. I think a humidistat is a distraction and not necessary as with a cooker hood most of the problem will be dealt with at the source. Providing it's used of course.
Replacing the air being extracted, particularly with fire doors fitted, is not so simply. Cold damp air pumped into that environment, which would be most of the time in this country, would only add to the condensation problem and the obvious solution would be an integrated combined system with a heat exchanger unit, as mentioned by others. However I suspect this would not be suitable or within budget.
So my solution would be a commercial grade cooker hood and extractor with an additional reversible extractor on the opposite wall. This would provide flexibility in being able to boost the extraction rate or provide colder air into the kitchen.
You might also suggest the revamp includes induction cooking as this will do away with most of the wasted heat that results from other forms of cooking.
Good luck.