At the age of 17 Shaw left his unpromising environment and through the influence of an elder brother already in America, joined the commercial house of George and Samuel Douglas in New York. He returned three years later and was made a junior partner in the firm’s London branch, in which he eventually became a full partner.
Shaw normally supported each successive administration, though he was an infrequent speaker. In June 1807 Perceval nominated him to the finance committee and he secured the House’s preference over Burdett. On 27 July 1807, as a dock company director, he defended the London port improvement bill. He objected to Combe’s London petition against the orders in council, 10 Mar. 1808, as unrepresentative of the meeting at which it was mooted. He said he was convinced that on this ‘as well as on the merits of his Majesty’s present servants, and particularly on the merits of the expedition to Copenhagen ... in the population of England 99 out of 100 were decidedly in their favour’. Whitbread ridiculed this piece of political arithmetic: Shaw, he alleged, had similarly approved of late ministers when they were ‘the present ministers’. Shaw sought and obtained a baronetcy from the Duke of Portland in 1809. After voting with ministers on the address, 23 Jan. 1810, he joined opposition in favour of the Scheldt inquiry, 26 Jan., 23 Feb., but reverted to government on 30 Mar. The Whigs listed him ‘Government’ at that time. He felt obliged to vote against Burdett’s committal to the Tower, 5 Apr., and to support his colleague Combe’s remonstrance against ministers’ refusal to allow the City address in favour of Burdett to reach the King, 7 May 1810, even if it was not supported by the majority of the livery. (He had shown no sympathy for Burdett in debate on 4 Apr. and had been criticized for hostility to him as sheriff in the Middlesex election of 1804.)
At the election of 1812 Lord Melville asked Shaw to stand for Kirkcudbright, but he refused. He appeared on the Treasury list of supporters after the election. From 1812 to 1815, he spoke mainly on London and mercantile subjects. On 16 Mar. 1813 he failed to steer the firearms bill through its second reading. He was the leading corporation spokesman against the London prisons bill, claiming that the City magistrates were already doing all they could to reform Newgate, 28 Mar. 1814. His colleague Curtis was active to the same end but Farington the diarist was informed that Shaw had ‘more cunning’ and ‘more ability’ than Curtis.
In 1815, under increasing pressure from his constituents, Shaw became more independent. He presented a common hall petition and supported others from London against the protectionist corn bill, 24 Feb. 1815; having sat on the select committees, he spoke and voted steadily against it. He rebuked Vansittart, 8 Mar. 1815, for telling the House ‘not to consider the opinions of furred gowns and golden chains as authoritative upon a subject like the present’. On 29 June 1815 he voted for the Duke of Cumberland’s marriage grant, having also opposed inquiry into the Regent’s expenditure, 31 May. In February and March 1816 Shaw presented and defended several London petitions against the renewal of the property tax, claiming that the whole city was unanimously against it; he accordingly proposed the substitution of a loan without interest and voted against it, 18 Mar. 1816. He had voted with ministers on the army estimates, 6 and 8 Mar., although he claimed to support military retrenchment on 25 Mar. He voted with ministers on the civil list, 6, 24 May. He did vote for Althorp’s motion against the leather tax, 9 May. In December 1816 he was active as a magistrate in suppressing the Spa Fields riot.
Shaw retired for health and business reasons at the dissolution in 1818; he had met with ‘considerable disappointments’ in winding up his ‘concerns in America’. He may also have thought little of his chances of re-election in the face of the increasingly radical complexion of the London livery, or grown weary of their dictation, and he can scarcely have pleased the friends of government. He died 22 Oct. 1843. He ‘never was known to have asked for or received either place or emolument for any of his numerous family and connexions, for whom he had otherwise to make provision’. He was, moreover, ‘at all times a pattern for the performance of his official duties, punctual to all his appointments, and precise in all his arrangements’. He died unmarried, but by a second patent of 1813 the baronetcy passed to his heir at law, his sister’s son John, who took the name of Shaw. Shaw was the patron of ‘many deserving young persons’: indeed ‘the walls of his drawing and dining rooms were crowded with the portraits of many of those objects of his patronizing care’.