Is the english site under the same domain? i.e. domain.com/englishsite/ If so, you should go to google webmaster tools and specify any content from that directory is specific to the region United Kingdom. This will take about 4-8 weeks normally but it seems to be getting quicker.
The site must have a complete grasp of the English language along with high PR backlinks from authority English sites.
If you target both local and international traffic for your website, you can create separate pages for the english and the local language like using a page with /en/ That way, both traffic could understand your site's contents also with local and English SE bot crawlers.