He was born in Felling, County Durham, the son of a stonemason and was apprenticed to his cousin, Thomas Barnes, a Northumberland coal viewer. From 1808 he became agent to Charles John Brandling, who owned collieries on his Middleton estate near Leeds and whose family came from Felling. From then until his death, Blenkinsop lived at Middleton Hall on Town Street, Middleton, built in the 17th century as the Brandling family's Middleton home (they used the far more modern Middleton Lodge when visiting from their Tyneside homes).
In 1758 the Brandlings had built a wooden wagonway to carry coal into Leeds, using horse-drawn vehicles, now known as the Middleton Railway. Not all the land traversed by the wagonway belonged to Brandling, and it was the first railway to be authorised by Act of Parliament, since this would give him power to obtain wayleave.
In the early nineteenth century, attempts were being made to employ steam power for haulage. Richard Trevithick had experimented with various models of steam locomotive, and in 1805 his work had culminated in an engine for the Wylam Colliery. The cast-iron plated wood rails were unable to take the engine's heavy weight, however, and the initial attempt to convert to steam locomotion at Wylam was abandoned. Work on the development of locomotive power continued nonetheless. A shortage of horses and fodder brought about by the Napoleonic Wars had made steam traction a more attractive proposition and encouraged further development. Moreover, edge rails, made entirely of iron, laid at Middleton Railway from around 1799, were stronger.
While many people, such as William Hedley, felt that adhesion should be adequate with a locomotive weighing around five tons, Blenkinsop was less sanguine. In 1811 he patented (No 3431), a rack and pinion system for a locomotive which would be designed and built by Matthew Murray of Fenton, Murray and Wood in Holbeck.
The general opinion of the time was that a locomotive would draw up to four times its weight by adhesion alone (assuming good conditions), but Blenkinsop wanted more, and his engine, weighing five tons, regularly hauled a payload of ninety tons. The first locomotive probably was Salamanca, built in early 1812. Three other locomotives followed, one later in 1812, one around 1813, and the last one in 1815. One of these three was named Lord Wellington, and the other two allegedly were named Prince Regent and Marquis Wellington, though there is no contemporary mention of those names. Similar locomotives were built for collieries at Orrell near Wigan by Robert Daglish under licence from Blenkinsop, and at least one other was built by Matthew Murray for the Kenton and Coxlodge Collieries at Newcastle-upon-Tyne. What should have been Blenkinsop's third locomotive had already been sent to the Kenton and Coxlodge Waggonway at his request. There, it seems to have acquired the name Willington.