Sorry, I'd normally be able to tell you how to get offer codes without purchasing the newspaper. See my post here:
http://www.theanswerbank.co.uk/ChatterBank/Question1289065.html
However the terms of the offer you refer to state:
"Readers who successfully claim Saving Mr Banks preview screening tickets
must present the page from The Mail on Sunday, with the ticket, and have ID available if required".
http://www.dailymail.co.uk/home/prmts/article-2487185/Be-Saving-Mr-Banks.html
So you MUST obtain a copy of the paper to validate the offer.
Since members of the Odeon Premiere Club can see the film before its official release date, it's likely that all (or nearly all?) of the Odeon cinemas will be participating in the offer. Find your nearest Odeon here:
http://www.odeon.co.uk/
(Put your cursor over 'Cinemas' and then use the postcode search).
Similarly it's likely that all of the Showcase cinemas will be taking part:
http://www.showcasecinemas.co.uk/locations/search