I have a .com website. It is a UK local business website. I find it in first page of google.com, but 2nd /3rd page for .co.uk . would it happens for domain name?
If you did good seo and your domain is old and your keywords competition is low then possible it will show. But mostly site show locally first and then after get traffic locally then other keywords boost
if you use domain co.uk that would be ranked more higher on local search engine. read this article about it : http://www.freedirectorywebsites.com/article/myth-of-domain-names-extension.php