I would like several devices on my home network to be able to use Apples’s Time Machine to save data on the same hard drive. To achieve this, can I connect a 4TB My Password HDD direct to my Plusnet Router, rather than to my desktop computer?
That will depend entirely on what your Plusnet Router supports.
Most routers only support a small number certain formats and capacities.
Best place to ask is a Plusnet Forum (link below) and specify what Model Number Plusnet router you have.