The opening sequence was shot in Parliament Square. Most of the Palace of Westminster was rebuilt after the fire of 1834; only Westminster Hall (behind the statue to Oliver Cromwell) is original. It was built by William II (who apparently complained on its completion that it was disappointingly small).
The rest of the module was shot at Stokesay Castle in Shropshire, one of my favourite places in England.
We visit Stokesay again in the resource, exploring life on the manor in the days of the Domesday Book - see 'The Medieval Manor'. It's well worth a visit - a real gem.