This may be just a false perception, but it seems to me that England has a surprisingly diverse set of accents and dialects of English spoken across the country. It also appears to be very dense and tightly packed; one can go just a few miles in any direction and find themselves in an area where most are speaking with an accent barely matching the area they had left. I'm curious as to why that diversity seems much greater than anywhere else in the English-speaking world. It would seem that with a country that small it would be difficult for the accents to remain largely heterogeneous over time, and yet that is exactly what seems to have occurred. Why?
This is such a widespread pattern cross-linguistically that historical linguists, when attempting to discover the geographic origin of a language family, will look first to the area of greatest diversity -- that is, the area that has the most languages from that family in the smallest area.
The reason that we see this pattern is that languages change over time. When people are separated -- and this can be because of geographic or social reasons, changes in the language of one group can no longer spread as easily to the other group, and so the languages diversify.
This has been going on in England for a very long time -- much longer than it has been going on in North America, in Australia, etc.
As for how people maintain diversity when you would think that they're too geographically close to other dialects, consider how you learn your language: from your close family and your peers. Most people still interact day-to-day with people in/from the same area. People can travel further and more often than in the past, and do come into contact with people of many different backgrounds, but if I live in a small town in the north of England, most of the people I see everyday will probably be from somewhere nearby. (There are exceptions to this, of course.)
In addition, there are social factors that can reinforce language diversity. In the same city (London, for example), you can have many different accents that are associated with different socioeconomic groups. This isn't because they never speak to people from other socioeconomic groups (though they may speak most often to family, workmates, etc), but also because our language can communicate important things about our identity. You are more likely to speak like the people you identify with.
Basically, contact with speakers of other dialects isn't enough to wipe diversity out. There are regions of the world even more linguistically diverse than England, like Micronesia, Burma, etc.