"I'm surprised at the driving license application assistance site - admittedly my only experience of the real DVLC site is for renewing my vehicle license, but it strikes me as one of the best designed and easiest to use sites around and the last place I'd need help."

While it's not strictly a scam, it comes close.
These sites (and they also exist for passport applications) pay Google so as to ensure that when you Google "Driving Licence application" their site comes out higher up the page than the official government site. A small percentage of punters are sufficiently misled to think they are the official site, and part with money.

While they do not claim to be the government site (that would be illegal), their business model is based on the careless mistaking them for what they are not.