Educated at Eton College and Christ Church, Oxford and after serving as private secretary to the Prince of Wales, Tyrwhitt was elected Member of Parliament (MP) for Okehampton in 1796. Tyrwhitt was responsible for the construction of several roads across Dartmoor, a hamlet called Princetown named in honour of the Prince of Wales, a prison for prisoners of war captured during the Napoleonic Wars now known as HM Prison Dartmoor as well as the Plymouth and Dartmoor Railway. He became Auditor of the Duchy of Cornwall in 1796 and Lord Warden of the Stannaries in 1803.