[3] Leveson matriculated at Queen's College, Oxford, on 10 January 1576, and studied for a time at Gray's Inn.
He was a close associate in Kent of William Brooke, 10th Baron Cobham, and eventually one of the executors of his will.
He was also a captain in Peregrine Bertie, 13th Baron Willoughby de Eresby's 1589 expedition to France.
He was knighted in 1589, and helped raise volunteers for three of Sir John Norris's expeditions in 1589, 1596 and 1601.
[2] While riding to his house at the Blackfriars, London, on 8 February 1601 Leveson inadvertently became instrumental in suppressing the rebellion of Robert Devereux, 2nd Earl of Essex, taking command of a force on Ludgate Hill and placing a barrier across the street.