How to get the best results link building?

I'm assuming your area pages are not independent websites but pages of your main site.
If this is the case, the PR of your domain will increase and also the authority of your site. That will help not only your homepage, but also the other pages of your site.

You've got solid advice above about building links to your internal pages as well as the home page. Deep linking is hugely important. Please ignore the advice that says build links only to your home page, it's bad advice.

No. You want people searching for "car hire manchester" to find the right page directly, so you want the correct page to rank for that phrase. The links pointing to the "Car Hire Manchester" page should have that anchor text and its variations (Manchester Car Hire, Cars for Hire in Manchester, and even simply "Manchester").

But one thing you should remember is that only the anchor text of one link from one page to another counts. If you have another link from the same page to the same other page, it will be ignored by Google. So one consequence of this is that if your pages are linked through global navigation, and the navigation links are indexed before any other links on each page, those other links are a waste. (A workaround for this problem is HTML content stacking.)

It's hard to understand exactly how your site is organized without further detail. As stated, your approach is OK so long as it makes sense for the users of your site and does not seem like spam to Google. For example, I would not have a lot of different pages such as "car hire Manchester," "hire a car Manchester," "hiring a car in Manchester" etc. You can still capture all those phrases by developing external links (backlinks) with anchor text variations.

That's fine (look at Wikipedia!). You should realize though that on-site SEO provides only a small part of what can be achieved with SEO. Its greatest power comes from backlinks, if you have access to the right kind.

That's reasonable, as stated. But always take SEO advice that's based on a mere description of what you are doing with a grain of salt. A description is not the same as actually seeing your site. One potential concern is how many links you have on each page. Google's official guideline is no more than 100. In my opinion you can safely do up to 200 if you must, but more than that might be a bad idea.

Your results can always be improved a lot through correct link development. One thing I hope you realize is that since you are targeting a specific regional market and need rankings in google.co.uk and even rankings for UK-based users of google.com, the UK, links from other countries will have a much lower value for you. You need links from sites that are physically hosted in the UK. Unfortunately, this makes correct link building much more difficult for you and renders free/cheap link building (e.g. forum posting, blog commenting etc.) even more useless than it normally is (and it's normally already pretty useless). This is precisely why "power SEOs" offer geo-specific and not generic global services: it depends on where they can provide links for (e.g. I routinely do the UK and the US, but not yet Canada or continental Europe). And by quality links i mean relevant one-way links from quality, high PR sites that are not scammy or interlinked in any way (no SEO netowrks). If you can get those from the UK, you're golden.

Good luck!