Is anyone aware of 'social classification' data sources used, for example, here:
The data on this site uses the sum of AB and C1 from the census 2011 social classification data.
It can be downloaded without charge from NOMISWEB (ONS). I think the particular dataset you are after is
LC6124EW (LC = Local characteristics; EW= England/Wales). You should also find the same dataset for Scotland suffixed
More info on the details of the classification can be found here
The specific classifications you refer to sound very much like MOSAIC data from Experian. We use this in Local Government and the classifications sound exactly like that. It's a commercial dataset though and it doesn't look like there are any free or open versions. Looks like that website uses a variety of sources but I would take a bet that MOSAIC is one of the primary ones.