@Lakotaubp I tried a fresh install of latest mint 19.3, trying the deb and appimage installers. It didn't work.
Then I removed the deb installer and installed the snap installer and tried that with the usb cable of a friend that had just arrived. Something different happened - the Ubports recovery was now installed but the next step of downloading UBports to the phone was not happening.
After retrying the installation several times it started to push Ubports to the phone but was losing the usb connection and halting with the error message every 30 seconds, so I just clicked "try again" each time and the process completed. Success, finally.
I suppose the issue from the start may have been usb cable, but I honestly tried 4 or 5 different cables and even my friends brand new one was losing connection.
Unusually, Ubports is now showing the phone as having 16GB total storage when it is the Oneplus One 64GB model.
Thanks for your input @Lakotaubp, I'll mark this as solved.
edit: How do I mark the post as solved? I think I read in another thread that new users cannot do that.