I went a slightly different direction - as of 2017, the UK driver is looking for deprecated dependencies - libtiff4, which depends in turn on libjpeg8.
Those are available here for libjpeg8 under wheezy, and here for libtiff4 under wheezy as well.
Once you have the UK driver, and these two packages into one directory, your commands will look something like:
sudo dpkg -i libjpeg8_8d-1+deb7u1_amd64.deb
sudo dpkg -i libtiff4_3.9.6-11_amd64.deb
cd cnijfilter-mg5400series-3.80-1-deb
sudo ./install.sh
The install script will then run properly and you should be able to answer the questions without any trouble. The network detection might take a second or two.
Solution works for: Linux Mint Debian Edition (Betsy), but should also apply to Ubuntu and other Debian distros based on the 3.16.0-4 kernel (wheezy).