Sir Robert Phelips (c. 1586–1638) was an English politician who sat in the House of Commons at various times between 1604 and 1629. In his later Parliaments he was one of the leading spirits in the House of Commons and an opponent of James I, Charles I and their adviser Buckingham.
Phelips was the son of Sir Edward Phelips and his first wife Margaret Newdigate, daughter of Robert Newdigate of Newdigate, Surrey. His father was Speaker of the House of Commons and Master of the Rolls. Phelips was knighted in 1603. In 1604 he was elected Member of Parliament for East Looe. He was travelling in France in July 1613, and in the same year was granted the next vacancy in the clerkship of the petty bag. In April 1614 he was elected MP for Saltash. He made his mark by joining in the attack on Richard Neile, then Bishop of Lincoln, for his speech in the House of Lords reflecting on the commons. In 1615 he accompanied John Digby afterwards Earl of Bristol to Spain, where Digby was negotiating the Spanish match. Phelips kept a diary of his movements for a few days (printed in Hist. MSS. Comm. 1st Rep. App. pp. 59–60), and wrote an essay on the negotiation, which is among the manuscripts at Montacute House.
In 1621 Phelips elected MP for Bath, and at once took a prominent part in its proceedings. On 5 February he accused the Catholics of rejoicing at Frederick's defeat in Bohemia, and meditating a second "gunpowder plot." On his motion of 3 March 1621, the house turned its attention to the patent for gold and silver thread. He served on the committee appointed to inquire into the matter, and brought up its report, which furnished the main charges against Sir Giles Mompesson. Alsi in March, he was chairman of the committee to inquire into the charges of bribery brought against Francis Bacon. On 17 March he presented the committee's report in a speech "of great force and moderation", and was ordered to lay the evidence before the House of Lords. In May he was one of the first to urge the house to punish Edward Floyd. In November he warmly attacked Spain, and proposed to withhold supplies and a few days later he supported the commons' petition against the Catholics and the Spanish marriage. On 1 January 1622 he was arrested for his share in these proceedings and was imprisoned in the Tower of London on 12 January. He remained there, in spite of his brother's petition, until 10 August 1622.