I've been thinking, and I think one thing that might contribute to people thinking there weren't many different British accents is that it used to be the norm for British actors to learn to "lose" their regional accent, and speak in what is know as RP (Received Pronunciation). For instance, you'd probably never tell from his accent that Tom Baker is from Liverpool. He doesn't sound it. In the past, you rarely heard a regional accent on telly, unless it was some character actor putting on a fake one. This changed sometime in the 80s or 90s, and now regional accents are all over the telly. But think of any big British actor from the 50s, 60s, 70s and it's a good bet they speak Received Pronunciation. RP is used by teachers in schools now too, even going back just 20 years to when I was in Primary school the teachers still had strong regional accents. I have noticed that kids these days seem to have more 'generic' accents than perhaps people of my generation and older. For example usually you can tell if somebody from here is from Aberdeen, or if their from the country, or from a fishing community all within a 50 mile radius or so. These days I think the younger folk mostly sound the same.