Green Party MP Caroline Lucas said she would prefer to spend time in Brighton than pay tribute to Baroness Thatcher.
The Labour MP for Rotherham Sarah Champion said Thatcherism "tried to destroy our town".
I'm not in Parliament today as I my time is better spent helping #Rotherham. Thatcherism tried to destroy our town & community, they failed!
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The prince laid a floral wreath at one of a group of metal crosses near Wellington Arch in central London.
The group, which also owns Premier Inn, said on Wednesday that it will pursue a ‘demerger of Costa’.
The showers will become more frequent as the day goes on, giving some heavy downpours in places during the afternoon.