You have several things going here. First off, you have to look at what was said about SEO over a timeline. Google does things then realizes it was wrong headed. You have to gauge what was said against reality. Sometimes what was true is no longer or really never was. SEO is really not nearly as complicated as people think it is. In this case, Google was working on GEO targeting and load balancing (see link below). What seemed to work was that IP addresses were an indicator for location using GeoIP techniques. But since IP addresses assignments change rapidly and GeoIP targeting has a error rate sometimes as high 10% or 20%, this turned out to be a bad assumption so the whole GEO location to IP address thing was discarded.
Having said that, there is no GEO location tied to an IP address. Yes Google did try this for a period and some effect still exists, but within the perspective of Spam and not Ranking. Here is what I mean. The IP address is evaluated and a score is applied to it in regard to stability which in effect is a good neighborhood and bad neighborhood score. Stability testing and scoring is a concept used in security mechanisms but applies for search too but with different parameters. To say that IP addresses have a GEO location effect for determining site quality that translates into the SERPs- that would be correct.
Let me give you an example.
Networks in China have a very poor reputation. In the past two years or so, .cn sites are being re-homed to better networks and moving their sites to the U.S., U.K., Denmark, and so on. This is because bad neighborhoods have an effect. Some of these sites use the Chinese language and are intended to be used in China. Most are company sites. But here is the point, even sites that have GEO targeting for Beijing for example may be using non-Chinese networks.
Now to your point that IP addresses in the U.K. may rank better. What is true is, sites hosted on U.K. IP addresses can rank better due to one particular metric that Google uses assuming that all other ranking factors are equal. Stability .aka. trust .aka. good neighborhood. So to say the effect is minor, would not be true. IP addresses matter. But it is not true to say that the IP address has a GEO location effect otherwise.
As far as having several IP addresses pointing to a single site, that would be possible but unnecessary unless you are homing servers in particular locations. Take Google as an example.
Here is a link to an answer I gave a while ago that is not fully related to IP addresses but ccTLD's that may be useful to you. Is it worth always geotargeting your site? It is not necessary to answer this question directly, but can broaden your perspective. The two are somewhat related at least historically.