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You are correct...on two counts... Wellington was also opposed to Catholic Emancipation too....UCL was the first university that was not aligned to the church... Wellington's reply was to support the creation of King's College, London.
Technically, the first Prime Minister was Campbell-Bannerman (1906)....before then they could be more correctly called the 'First Minister' but most holders going back to Robert Walpole in the mid 18th century are often regarded as prime minister.
Or indeed any history at all: The Duke of Wellington strongly opposed Jewish emancipation. But some probably wouldn't class him as a 'Prime Minister' as we know it.