Humidity is the biggest issue for a subject of the UK, I'd think, since the temperature is fine most of the time (at least from the perspective of a playing card). Try a simple dehumidifier in a room with the doors and windows closed most of the time. You only have to remember to empty the water trap regularly.
Cupboards might not be ideal, due to the fact that often they're against an exterior wall rather than an interior one.
Oh, I just had an awesome idea!
Try this:
https://www.spacebag.com/17/index.dtm?mid=563894It's airtight, watertight and resists pests. Toss in a few silica packs and you're good to go. There's a way to reuse the silica packs - they stop absorbing humidity after a while, when they get fully saturated - probably by heating them.
Best thing about these bags is that they're pretty cheap. I used to use them when traveling to make things fit better in the suitcase, but there's a catch to that: you're removing the air, but not the mass! Fill a suitcase with a few of these bags filled with clothes and it will weigh a ton.