Before his call to the bar, Marsh joined the Whig Club, 13 Jan. 1795, and was a contributor to The Cabinet, published at Norwich that year. He practised at the Norfolk sessions and in 1802 was complimented for his impartiality as sheriff’s assessor in the county election. By then he was an admirer of William Windham, whom he informed, 11 Nov. 1802, that he was about to publish a pamphlet in vindication of his political conduct. The first edition, if faulty, was successful and Windham helped him with an improved second edition in 1803. It was entitled An appeal to the public spirit of Great Britain. Through Sir John Coxe Hippisley, another friend of Windham’s, Marsh obtained an Indian judicial appointment in 1804; it may be that Windham found a ‘highly advantageous’ situation for him at home—if so, it did not prevent his proceeding to Madras. Before he went, he submitted to Windham part of a pamphlet written at Hippisley’s behest, critical of the narrow basis of Pitt’s second ministry and favourable to Catholic relief. This may have been published in 1805.
In Madras Marsh did ‘very well’ and was thought to be making a rapid fortune. So Lord William Bentinck, to whom Windham had commended him, wrote of him, 11 Mar. 1807, adding, ‘He is I am told somewhat more irritable than is suitable to these torrid regions. He is indefatigable, very able, and highly honourable.’ It was his ambition to become a puisne judge at Madras and on 25 July 1807 he reminded Windham of this wish expressed to him about two years before; but Windham was by then out of office. Marsh pointed out that he sought the honour only, as it could not increase his income.
At the first general election after his return to England, Marsh tricked his way into Parliament. He appeared at an opportune moment at Retford, where the 4th Duke of Newcastle’s interest was in disarray, as a friend of the Marquess Wellesley. He deceived many electors into believing that he was the Whig candidate and when the latter (George Osbaldeston) arrived, professed to be a ‘Foxite’. Osbaldeston described him as ‘a clever fellow, a good speaker, with plenty of assurance’, though ‘a perfect stranger to me and also to the people’, but he managed to find sponsors. In any case there was no contest and according to their agent Oldfield the Members did not settle their accounts with him.
Marsh behaved as a Wellesleyite in his first session, voting against the bank-note bill, 14 Dec. 1812, against the vice-chancellor bill, 11 Feb. 1813, and for Catholic relief throughout. His maiden speech, 1 Mar. 1813, was in favour of relief. He steadily opposed Christian missions to India at the end of the session, delivering a long philippic (afterwards published) against them on 1 July. In it he vindicated the ‘national character of Hindostan’ against ‘a fit of absurdity and fanaticism’. After the break up of Wellesley’s squad, he supported the ministry. He was a forthright critic of the clause in the copyright bill requiring 11 copies of all books published to be awarded to the universities, 18 July 1814. On 27 July he gave notice of a motion against the conduct of Sir George Barlow in Madras which he had scrutinized unfavourably in a pamphlet the year before. While it was he who the same day presented a Norwich barrister’s petition against General Gore, governor of Upper Canada, it would appear that the reporters wrongly attributed to him a further motion on Canadian affairs, 28 Nov. 1814, which was that of George Philips.
In May 1815 Marsh was rumoured to be returning to India with a fresh appointment, but nothing came of it.
Marsh contested Sudbury in 1818 along with his friend Hippisley, but, arriving late, was left at the bottom of the poll. In 1823 he was in such financial straits that he wrote from France to Robert Peel, whom he scarcely knew, for a loan of £50. In 1831 he was an unsuccessful candidate at Petersfield. He died abroad in obscurity in the spring of 1835. He was the reputed author of two volumes of gossip entitled The Clubs of London (1828). His son Hippisley (1808-84) became a colonel in the Bengal army.