That might be a VDSL product from any of the popular ISPs (if you live with a few hundred metres of a "green box"), a cable product if you live in one of the cities or larger towns that have cable, or dedicated fibre link.

Some people see significantly worse performance because of their own suboptimal choices (e.g. maybe the blinking lights on the supplied VDSL modem annoy you so you run a telephone extension to a different room and lose 4Mbps of bandwidth because crappy telephone extensions don't do high bandwidth networking very well) and over a population of millions some will see physical network problems, that may need repair before they see the intended performance. But on the whole this 30Mbps coverage figure is based on extrapolating measurements from real users over data about available service.

I'm not aware of any 16MB/s products (16MB/s = 128Mbps or maybe you just meant 16Mbps) but Lewisham, which you gave as an example, has VDSL available at all the consumer nodes, so unless you lived in the £5M penthouse of some mixed use building in Docklands you could have bought faster networking you just didn't.

It can seem like surely if they could offer 30Mbps VDSL, why is my ADSL only 1Mbps? But that's misunderstanding the technology. ADSL was deployed in the UK to exchanges, so the signal needs to get from your home to an actual telephone exchange, there's probably one in your borough but it might be well over a mile away. However VDSL is in street cabinets, so your signal only travels to the cabinet which might be only a few hundred metres away. This makes it somewhat more expensive but also a lot faster. Unless (in both cases) you don't buy it.