Thanks for all the information so far...

I think I'll get one of the dust extractors I linked to in my first post. Will it definitely be powerful enough to pick up the fine dust? I'm thinking of connecting the output to a 'lean to' outside the workshop with a bin underneath. That should avoid the problem of fine dust getting through the bag.

I've got a big fan somewhere that might be suitable to make an air filter, so if necessary I can do that.