Markham’s father died when he was still young and his position in his early years was weakened by the dislike of his grandfather, who disinherited him as far as he could. The plate and furniture at Cotham, and all the houses and lands that were not entailed, went to his grandfather’s sons by his third wife, and Markham had to refurnish Cotham when he inherited the estate. He was described as a ‘favourer of religion’ by the archbishop of York in 1564 and in April 1565 he was one of those whom the Privy Council asked to take special care in assessing the subsidy. His name occurs a number of times in the following years in connexion with local administration. He and Sir John Byron produced a list of Nottinghamshire recusants in 1577, with the value of their property, and in 1590 Markham was amongst the local justices to inquire into complaints of engrossing in Nottingham.
Sir George Chaworth, Markham’s cousin, was a relative and henchman of the 3rd Earl of Rutland, and Markham himself was a follower of the Earl. He owed his return to Parliament for Grantham to Rutland, who was granted both nominations by the borough in that year, and Rutland was no doubt behind his election for the county in 1571. Although Markham was still a follower of the Rutlands in 1588, when he was an assistant at the 4th Earl’s funeral, during the long minority that followed he became a follower of the earls of Shrewsbury, and his third son Gervase became the champion of the Countess of Shrewsbury. Before the election for the 1593 Parliament Robert Markham had the backing of the 7th Earl of Shrewsbury for one of the county seats, but he withdrew before the election and in the event never sat again. In the 1586 and 1589 Parliaments Markham was active. On 21 Nov. 1586 he asked for advice on dealing with the claim for wages made against the borough by his predecessor as MP for Grantham, Arthur Hall. He was named (2 Dec.) to the committee set up to deal with this. The following 10 Mar. he was on the committee of the bill about East Retford, and, 18 Mar., he was one of those appointed to attend the Queen to hear her thanks for the benevolence just granted. In 1589 he was appointed to committees dealing with returns (8 Feb.), purveyors (27 Feb.), Lincoln (11 Mar.), the debts of Thomas Hanford (18 Mar.) and glass making(19 Mar.). On 21 Mar. 1589 he introduced a motion ‘on behalf of Mr. Aylmer’. As first knight for Nottinghamshire he was also entitled to attend the subsidy committee appointed on 11 Feb. 1589.
Markham was frequently at court. Through his grandmother he was descended from the Beauforts, and was thus distantly related to the Queen. She called him ‘Markham the Lion’. But his expenses at court forced him to sell the park at Maplebeck, Lincolnshire, and he was in debt at his death, intestate, on 20 Nov. 1606.