What I didn't say was that the internal telephone wiring goes from the master socket to several extensions both upstairs and downstairs, and the modem was plugged into the last one - furthest from the garage. I have both shortened the copper path, and removed potential interference.
The modem isn't in the garage because the WiFi signal can't get to the whole house from there (& there isn't a convenient power socket either. Ideally I should have a modem in the garage and run a cat5e cable to an AP in the house. At the moment I don't have the right equipment to do that, but I do have spare telephone cable.
Sorry for the confusion. Maybe I should edit I have edited my earlier post, to clarify the original layout.