Its a bit like a water pipe, you are limited to the slowest connection in the chain, also sites may limit the speed at which you can download to preserve their bandwidth. But I do agree i think 60K is more than I have every been able to get going.
The 512K quoted for the broadband connection is probably quoted in Kbits/s and the 60K is probably in Kbytes per second. 8 bits in a byte so 512Kbits/s divided by 8 = 64Kbytes/s. So 60K is pretty good, i think most people, myself included see only around 45-55Kbytes/s on a good day.
I was led to believe that because I live in a block of flats we would have a slower connection (due to the amount of boxes sharing the line) . This certainly isn't the case however, and we regularly clock up speeds of 80kb/s on things like kazaa...
NTL runs at 600Mbits not Kbits. They origionally offered %12Mbits but upgraded everyone free so that Telewest couldnt say they had a faster 'Standard connection'