The computer-built search engines continually trawl the net, finding sites and building up a database of sites with the keywords that are hidden within the web pages. The human-edited directories are more like the Yellow Pages. The directory editors decide which sites to include and list them under appropriate category headings. Each category has an editor who decides which appropriate web sites to include. Each category has subcategories, and so on.
Many search engines have a UK-based version as well as versions based in other countries.
It is generally better to use the Uk version, as you're more likely to find results that are specific to the UK, but you might want to widen your search by using an international version. Most search engines will give you a choice of searching only UK sites or searching the whole web. Try them both until you get a feel for it. The search engine should tell you how many results it has found. Results are improved even further if you put phrases in quotation marks.