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We have a couple of mature eucalyptus trees (pollarded a couple of years ago, and back to 10-15m-ish tall now) that we'd like to build a 7x4m garden room under. Ideally about 1m away from the trunks.
Is this an awful idea?
Depending on your soil, you might need deeper foundations than you expect (which could bump the cost up). Also worth noting quite a few gums can be prone to just randomly dropping branches for no reason. So the roof might need designing to suit!
Our eucalyptus blew down, so yes, it's a ridiculous idea!
😉
If you dig foundations that close the tree(s) are unlikely to be too happy about that. If they do fall they will likely fall away from your garden room due to the lack of roots on that side. Unless you do some  sort of pile foundation.
Which eucalyptus?
It'll depend on the permanence of the building.
Eucalyptus tend to be very deep-rooted to get water during a dry spell. They can easily out-drink dry summer rainfall which might cause ground problems, they then slow down about now, which coincides with greater rainfall and reverses the dry soil