A Roman Catholic, like his friend and fellow collector Charles Townley (who would encourage Blundell's collecting and introduced him to the antiquary Thomas Jenkins), he was thus barred from the British university system, and he was educated in France at the college of the English Jesuits at St Omer and the English College, Douai.
In 1760, he married Elizabeth, daughter of Sir George Mostyn, bt, of Talacre, Flintshire (commissioning her portrait from Joshua Reynolds).
His high income from various sources enabled him to collect classical sculpture and old master paintings (including ones by or after Poussin, Ruisdael, Brueghel, Jacopo Bassano and Andrea del Sarto, and a copy of Veronese's The Wedding at Cana, commissioned during a visit to Paris), to improve Ince Blundell Hall and to buy and commission artworks from current artists like Richard Wilson, Canova, Gavin Hamilton and Anton Raphael Mengs.
In 177,6 he went on a Grand Tour to Italy, visiting Milan, Venice, Ancona, Rome and Naples.
He tended to collect wholesale rather than discriminatingly, as with his group from the Villa Borrioni (probably also in 1777), and also knowingly purchased modern copies by Giuseppi Angelini and Carlo Albacini and others and classical works imaginatively restored by dealers such as Bartolomeo Cavaceppi and Giovanni Volpato.