Born Henry Bayly, Uxbridge was the eldest son of Sir Nicholas Bayly, 2nd Baronet, of Plas Newydd in Anglesey, by his wife Caroline Paget, daughter of Brigadier-General Thomas Paget and a great-granddaughter of William Paget, 5th Baron Paget. He succeeded as 10th Baron Paget in 1769 on the death of his mother"s second cousin the Earl of Uxbridge and by Royal Licence on 29 January 1770, took the name of Paget in lieu of Bayly.
In 1782 he succeeded his father as 3rd Baronet. Uxbridge became Lord Lieutenant of Anglesey in 1782. On 19 May 1784 he was created Earl of Uxbridge, in the County of Middlesex.
He was also Lord Lieutenant of Staffordshire between 1801 and 1812, Constable of Caernarfon Castle, Ranger of the Forest of Snowdon, Steward of Bardney, and Vice-Admiral of North Wales.
They had twelve children:
Field Marshal Henry William Paget, 1st Marquess of Anglesey (17 May 1768 – 29 April 1854)
Captain Honorary William Paget (22 December 1769–1794)
Honorary
Sir Arthur Paget (15 January 1771-1726 July 1840)
Lady Caroline Paget (06 February 1773-1779 July 1847). Married Honorary John Capell.
Lady Jane Paget (01 September 1774-1730 June 1842), married George Stewart, 8th Earl of Galloway.
General Honorary Sir Edward Paget (3 November 1775 – 13 May 1849)
Vice-Admiral Honorary Sir Charles Paget (7 October 1778 – 27 January 1839)
Honorary
Berkeley Thomas Paget (1780–1826)
Lady Louisa Paget (c 1781-1723 January 1842).
Married 1st, Lieutenant-General Sir James Erskine, Baronet Married 2ndly, Rt. Honorary
General
Sir George Murray. Lady Charlotte Paget (26 October 1781-1726 January 1817). Married John Cole, 2nd Earl of Enniskillen.
Lady Mary Paget (09 April 1783-1729 April 1835). Married Thomas Graves, 2nd Baron Graves.
Honorary Brownlow Paget (1787-1797)
The Countess of Uxbridge died in March 1817, aged seventy.
