England was settled by a lot of different people groups who brought in their own languages or dialects, all variants of early Low Germanic. As time passed and those languages turned into what we call Old English, regions held onto aspects of their languages that are now similar enough to just be called accents.

If you look back to Old English, at the earliest records dating back to about 700 CE, you see four distinct dialects crop up: Northumbrian, Mercian, West-Saxon, and Kentish. They roughly correspond to where the Angles, Saxons, and Jutes settled (the Jutes are why Kent has one of the most distinct dialects). Britain had a lot of other factors shaking things up early on. In the east, it was common for Scandinavian people to raid, conquer, and settle, so Old Norse affected the folks up in Northumbria especially (both it and East Anglia fell under the Danelaw, but Northumbria has always been prone to a fast-evolving dialect). England might have started standardizing the court language out of London more like France did from Paris, but the Normans took over and pretty much cleaned house among the nobles, ensuring a thoroughly Norman French-speaking ruling class, so English evolved among the peasantry for a long time. The Normans weren't interested in talking with their new subjects, so Norman French didn't have much of an impact on the dialects--yet. After a few generations, though, the "Norman" rulers in England started seeing themselves as different from the Normans back on the continent, so the "Anglo-Normans" started to look and sound more English. Wars with France made that sense of nationalism bigger and led to English being used in the courts in the 14th century, which is why we have a lot of French in our modern English today. But notice that the French influence is pretty uniform across all England--one brand of French peppering four brands of English. London's East Midlands dialect (you can see that in Chaucer) starts becoming the "standard" for the whole country, but the history of diversity is fresh enough that they're still distinct accents today.

All that applies to England, mind. Celtic languages didn't impact the language very much because when the Angles, Saxons, and Jutes moved in, they moved in and totally displaced the Celtic natives. Where the Scandinavians settled and mixed, the Celts just got pushed out, so there wasn't much early language borrowing on either side to affect accents

If you're in America, you might be confused about why our accents aren't even more diverse. That's mostly because the Europeans who came over here started off as a really mobile society, and we never really stopped being mobile. People traveled more, people mixed more from the get-go, and we've been historically more spread out, so you don't see the same distinct pockets of dialects as much in contrast. Interestingly, our English has been evolving more slowly than England's.

Mitchell, Bruce and Robinson, Fred. A Guide to Old English 8th Edition (2012). Baugh, Albert and Cable, Thomas. A History of the English Language (2002).