The only real difference between country search and the whole web search is the competition. However, that may be more complex than you'd think at first. It's not like the country search simply filters the sites from other countries out of the web results. There is a lot more to it.
Google's algorithms have a lot of variables that depend on the information they get out of their index. That means that a page can be within the limits in country search but outside the limits in the whole web search. Let me use a simplified example:
In a specific country a keyword can have an average
PR of its selected pages of 3, an average backlink anchor text age of 3 months and your site can be close enough to those values to rank happilly in the top 10.
On the whole web that same keyword can have an average
PR of its selected pages of 4, an average backlink anchor text age of 8 months and in this case your site is not within the limits and you´re ranking much lower or even not at all.
It's a whole different ball game when you compete with the whole world. The standards are not the same and unfortunately for the UK, the english language is spoken by more than 2 billion people. So competition in the whole web is pretty big.