I did a Tracert and it seems to be average throughout, no large spikes anywhere. I've never had lag like this before, see below for an example of what happened when I tried to take a mission:
Problem solved: My mum pretending that she knows how to use a computer. After spending 20 minutes arguing with me, I showed her how she had totally screwed up the router and fixed it, at which point she got very stressy and told me I knew nothing.