Q: Can't connect to the account "hotmail.co.uk".

What OS version are you using? You posted in Yosemite, but your profile shows El Capitan.

Try deleting/adding back the account.

Mail El Capitan

Mail (El Capitan): Mail troubleshooting

Mail (El Capitan): If you can’t receive messages

Mail (El Capitan): If you can’t send messages

Mail not sending or receiving messages after updating OS X

Mail Yosemite

Mail troubleshooting - Yosemite

Mail (Yosemite): If you can’t receive messages

Mail (Yosemite): If you can’t send messages

Mail not sending or receiving messages after updating OS X

I had a similar problem. Wouldn't verify my account or connect or accept my username password. Found out that Hotmail/Outlook have change the settings to IMAP, so if you've had your mail setup originally with POP then it won't communicate. I've tried everything apart from... Logging into Outlook, go to settings and then select options. On the left hand side menu is POP and IMAP, click on this. Then under POP options click Yes. Go back to Mail and re enter our password and....... Hopefully it works, it did for me

I have the same problem.  Everything was working fine until a few days ago when the Mac Mail would not speak to Hotmail.  Mine is an old hotmail.co.uk address.  I have tried deleting the account from Mail, then reinstalling both as an exchange and as a mail account.  I have also changed from IMAP to POP in the Outlook settings through the web browser to no avail. 

Have you managed to get yours working?