They were also running TV adverts at the time claiming they had detector vans about, and if you didn't have a licence you'd be caught. I did some research at the time, and it seemed that evidence from a detector van had never been submitted as evidence in court cases for those without a licence.
It didn't take long to realise in the age of databases, it's easier just to send out scary letters to all address without a registered licence and hope there will be some 'conversion rate'. The effort required to actually chase on this seemed disproportional to the benefits.
And for those wondering, I did have a licence, it's just the address the BBC had for the flat was subtly different to the one on the bit of paper. I had hoped that they would follow up with a more detailed investigation, so I could see how it worked and ask about the vans, but they never did.