Thomas was a member of the old Reading family of Blagrave. He was the eldest son of Richard Blagrave - the younger half-brother of John Blagrave, the Mathematician - by his third wife, Anne, the daughter of Thomas Mason of Northwood on the Isle of Wight in Hampshire. Richard and his brother- and father-in-law were all musicians at the court of King Charles I. Thomas' younger brother, Robert, followed him as a wind player and violinist at the Royal Court.

As early as 1637, when Thomas can only have been about fifteen, he was already deputising for a sackbut player named Edward Bassano and, the following year, he joined the hautboy and sackbut ensemble, assisting his father there until he achieved a full post upon the former’s death in 1641. Despite joining Cromwell’s musicians after the Civil War, Blagrave was apparently “a great sufferer for loyalty in the late rebellion”.

Blagrave was quickly sworn in as a court violinist at the Restoration and his name occurs among the Gentlemen of the Chapel Royal at the Coronation of King Charles II, on 23rd April 1661. About 22nd October in the following year, he was appointed Clerk of the Cheque there. He was also a member of Charles II's private band of violins, and Wood says that he was “a player for the most part on the cornet-flute, and a gentle and honest man”. He was certainly recorded as a wind player at Windsor Castle in April 1661 and, by August, he had regained his pre-war position.

Samuel Pepys became friendly with Blagrave and his name occasionally occurs in his Diary, on one occasion having been given a lute by the writer. He visited him at “his old house in the Fishyard” in St Margaret's Lane, Westminster (although in 1664 he also had a property on the north side of the Strand). On 7th March 1662, Blagrave arranged for Pepys to obtain admission to the Chapel Royal in Whitehall and, after Blagrave was appointed Lay Clerk of Westminster Abbey in August 1664, the same chronicler records that he had been “with Mr. Blagrave, walking in the Abbey, he telling me the whole government and discipline of Whitehall Chapel, and the caution now used against admitting any debauched persons” the following month. In 1666, Blagrave succeeded Christopher Gibbons as Master of the Choristers at the same Abbey and Pepys described him as “a sober politique man, that gets money and increase of places”. He held the post for four years. Blagrave is unfortunately mentioned as one of the King's 'musick' at whom Pelham Humphreys laughed on his return from France in 1667, saying that “they cannot keep time nor tune, nor understand anything”. A few of his songs may be found in contemporary collections, such as ‘What conscience say it is in thee’ and ‘What means this strangeness’. He sang as a countertenor, as at Windsor Castle in 1674, but also as a bass, as at the Coronation of King James II in 1685. This new monarch removed him from all his posts, but he retained his place in the Royal chapel.

On 14th October 1645, Blagrave had married, at St. Margaret's Church, Westminster, Margaret, the daughter of Thomas Clairvaux of Parson's Green in Middlesex. They had no children and, when he died on 21st November 1688, he left, to his widow, his house and lands at Teddington, while bequeathing various sums to his kinsmen, amongst whom were another Thomas Blagrave – possibly the son of his half-brother, Cheney – and John Blagrave, “my brother Anthony Blagrave's youngest son” – a violinist and the son of his full brother who had moved to Norwich in Norfolk. Thomas was buried in the north cloister of Westminster Abbey and his widow joined him a year later.

Edited from Leslie Stephen's 'Dictionary of National Biography' (1886).