You can find out the names of all the directors of a company at Companies House for a small charge, but not their email addresses.
Go to the Companies House website at
http://www.companieshouse.gov.uk/, go to WebCheck on the right, click through to the details of the company, and from there you can order information on that company. You would want the Current Appointments Report, which costs £1.00.
Once you have the names, you can probably guess the email addresses. You know the domain, and there are probably only around 10 common ways of writing any name as part of an email address.