adder - 3:31 pm on Aug 21, 2013 (gmt 0)
I would suggest the first email that goes out to them is written in a slightly nicer tone. I've found from my own experience in link removal that the majority of people comply when you ask politely (strictly but politely)...
The thing with .co.uk domains is that (thanks to British Govt.) anyone anywhere can register them. So, over the years, there's been a lot of abuse. You might be talking to some guy living million miles from you with a different culture and attitude.
Pissing him off simply makes your task of removing links more difficult. Besides, what legal action can you take, if say, I decide to link to your site? It's my choice :)
So yeah, try that first and then if there's no response, then follow up with a nastier message.
Just out of interest, have you checked what type of links are they? When you go to the detailed view of the link source in your WMT. It should show like "The XXX top links from Example.com"
To answer your question, theoretically, yes, it can affect your performance depending on what type of backlink profile you have. If you have like a dozen of links from low-authority sources and you suddenly get 80,000 links from a spammy site, then it may rise a few eyebrows, although this is unlikely. That's why I was asking about the kind of links you've had from that .co.uk website. Do they look like self-created manipulative links?
To remove them from WMT, you simply get the site to remove the links and then wait for a WMT refresh, which can take a long time to happen.
Do you know when the links were created? I mean, if you go to "Download latest links", do you see some links from that website?