What are the circulation figures in the UK and Europe of the Hong Kong
based publcations, East Daily, Apple Daily, Ming Pao Weekly, Sing Pao
Daily News, East Weekly and The Sun (not the UK version), broken down
year on year since 1980?

That's a tough one! You might start by sending a query to the Hong
Kong Audit Bureau of Circulations:
http://www.hkabc.com.hk/ 

The site claims the HKABC "provides an independent system of
validation of circulation figures, ensuring that the claims and
comparisons of circulation figures of member publications are
accurate, objective and comparable."

From the home page you can access audited circulation reports for
January 2000 through December 2003, but you will have to inquire as to
whether reports dating back to 1980 exist. There is a button for
sending enquiries at the top of the page.

Good luck!

Thanks but I have already tried the HK Audit Bureau of Circulation and
they couldn't help me - they only have details of figures in HK. I
look forward to your further comments, and hopefully an answer in due
course. Thanks!

OK, here's another suggestion, forwarded from a contact. Approach the
distributor(s) of these publications and see if they can provide you
with any statistics. They'd need to keep stats in order to know how
many copies to ship, whether their market is growing outside of Asia,
etc.

As a starting point, try the Overseas Courier Service, which is a huge
distributor of Asian titles:
http://www.ocstracking.com/

You could also ask for the names of their competitors, if they are
willing to say, which would provide you with additional sources to
contact.