Tricky one
The 1662 Visitation of Notts, cited by HOP, says father of John was the Francis killed in battle of Preston 1645 - which is wrong, battle was 1648. 1645 was too early for John to have been born.
Visit also says this Francis was at Magdelen Oxford, matric 1635 at age 17, gives him birth date of 1618. High Sheriff 1645.
BUT while the profile here for Francis MP lists his father as John Thornhaugh, the Visitation says it was a prior Francis, High Sheriff 1637, son of Sir John previously High Sheriff, who went to Cambridge 1605.
So I think you've nailed it.