Hi there,
from what I understand of your premise, you are asking whether you should create multiple backlinks from the same sources to each of your 20 pages. There are 2 issues you have to contend with here:
- Backlink density and propogation
As far as acquiring links goes, the key factor here is not so much the number of links you acquire, but the quality they provide your site. After gaining a link to your domain from another domain, the value of future links to your domain from the same domain diminishes, making this an extremely poor expenditure of resources on your part. For example, Google wants to see multiple domains linking to individual pages on your site rather than the same sources connecting to your site over and over on different pages. This approach is just more natural in its appearance.
Here is an updated guide to general link-building. I think this would do you some good:
http://moz.com/blog/category/link-building
- Backlink locality
Since you operate a website purely in the U.K., links from outside your country will likely be less relevant geographically if they come from other countries, but the pages being linked may not matter. For example, blogs involving tips to fix a leaky faucet or a clogged drain are likely to be equally valid regardless of who writes them or from where. On the other hand, if your site is attempting to find customers for a plumbing client of yours, it doesn't make sense to get links from plumbing material manufacturers in Texas if you work in the U.K.
To illustrate this, here is a personal favorite of mine from Rand:
http://moz.com/blog/10-illustrations-on-search-engines-valuation-of-links
See also:
http://moz.com/blog/are-on-topic-links-important-whiteboard-friday (on-topic vs. off-topic links)
In short, stick to 1 link per domain to your site unless there is something extremely relevant to your site and you feel the extra effort of building that link is worth it. Links built from UK sources are likely to be more valuable to your overall, but you can also find relevant information and data from international sources depending on the topic (in this case, informational pieces, perhaps in regards to DIY plumbing projects).
Hope this helps and feel free to follow up with further questions,
Rob