Too many air bricks?

[RedHerring2]

You do need to be aware of the need for ventilation as well, but hopefully, preferably controllable ventilation.

Hmm. I'm not actually aware of any other ventilation......./
/...........Our bathroom suffers from quite a bit of condensation and our bedroom windows sometimes have some condensation.

This is exactly what I was referring to. The current draught coming from the solum is adding to your general ventilation and if you reduce that you may need to provide additional ventilation elsewhere, e.g opening windows, trickle vents, extractor fans, etc. But at least this is controllable / targeted ventilation for as, when and where needed.

We have 2 gas fires in open chimneys which I think we've briefly used about three times in the 4 years we've been living here.

I think if these appliances are under 6kw they don't need additional ventilation. Try a search to check on this value. Excellent post here: //www.diynot.com/forums/viewtopic.php?p=1775628#1775628

These rooms are upstairs though, so shouldn't there be separate ventilation upstairs? (I should probably pop around the house and have a look for upstairs air bricks)

Not neceassirly. If I had any open vents (obviously excluding solum ventilation) I would block them up but replace with controllable ventilation as already mentioned. Condensation is a good indicator, especially if you have double-glazing, when you need to increase the ventilation.

Also, don't forget the general daily living practices, such as drying clothes indoors, no ventilation in bathroom after showers/baths, cooking, physical activity, etc all contribute more or less to humidity indoors. Excellent factsheet here:
http://ww2.reading.gov.uk/documents/Housing_and_Benefits/Housing factsheets/NScondensation.pdf