The emails seem to go to the contact email address in the WHOIS data. In my case, it would have been my old Demon email address that's been dead for over a decade.
The email should come from the registrar, with a link for you to click to verify the email address is correct.
http://www.icann.org/en/resources/compl ... rificationWhat happens if you don't verify your email is that your site will go dark, and will be replaced by a placeholder page saying that it needs verification.
So check the WHOIS data for any domain you own, make sure it's all upto date. If it's not, your registrar should provide a facility for you to correct it. You should contact them about this.
Even if your ISP and registrar are the same entity, this will still need to be done. It's ICANN being picky and making sure that the data is all up to date.
.co.uk is a different authority, so that should not be affected. Still work making sure that all is in order, just in case Nominet decides to go down the same route.