Just an update. So the bike is stored now in the garden. A WD40 cap just fits over the exhaust, with a acf50 soaked piece of rag in between.
Then I bought a new breathable cover, Oxford protex, but that doesn't breathe very well! I lifted it up one day to find the bike absolutely soaked of condensation
So I bought a tubular heater and placed it underneath. The cover almost reaches the ground, so heat is kind of retained and it warms it up only 1 or 2 degrees, but it's just enough to keep everything nice and dry above the dew point. It works a treat! So if you don't have a garage and you're looking for an inexpensive dry place, get yourself a 25 pound tubular heater