Smith was the son of a wealthy banker in Nottingham, also called Abel Smith (c. 1690-1756), and followed him into the same business. (By the end of the century the family bank was one of the biggest in England). He entered Parliament as member for Aldborough in 1774, and later also represented St Ives and St Germans. These were all pocket boroughs, and Smith may well have had to pay considerable sums to the proprietors to secure his seats; later a proportion of the family wealth was devoted to buying the Smiths a couple of pocket boroughs of their own, and by the early 19th century his son, Lord Carrington, could nominate the MPs at both Midhurst and Wendover.
Smith seems to have become an MP as much with the business advantages in mind as with any high political ambitions. Brooke quotes him as writing, shortly before he was first elected in 1774, "I see many solid advantages accruing to my family from a seat in Parliament, the best of which, the article of franking [the right to free postage, valuable in those days of heavy postal rates], will save a very considerable expense in so extensive a business as that I am engaged in." Although he supported the government, his first two speeches in the House of Commons were both attacks on the government for the way in which they had allotted subscriptions for government loans, in each case referring to occasions when his own firm had been excluded.
He married Mary Bird (c. 1725-1780), and they had eight children, several of whom followed their father into Parliament:
John Brooke, The House of Commons 1754-1790: Introductory Survey (Oxford: Oxford University Press, 1968, reprinted from Volume I of Namier & Brooke, The History of Parliament: The House of Commons 1754-1790, London: HMSO, 1964)
Lewis Namier, The Structure of Politics at the Accession of George III (2nd edition - London: St Martin's Press, 1961)
Abel Smith Last Will and Testament November 12, 1785. Public Record Office catalogue Reference: Prob 11/1168