Rastrick was born in Morpeth and attended local schools; at age 15, in 1795 he was apprenticed in his father's practice. Later, while at Bridgnorth, Shropshire Rastrick helped Richard Trevithick develop his ideas for the high pressure steam engine and locomotive, and later he was to testify in a parliamentary enquiry that he had built the locomotive that had been demonstrated in London in 1808. He also produced much equipment for Trevithick's abortive South American adventure.

In 1829 Rastrick was commissioned with James Walker to report on the economics of using either rope haulage or locomotives on the new Liverpool and Manchester Railway. After extensive travels to view the early railways of the age, their report favoured rope haulage on economic grounds! They did however include the rider that there were some benefits to locomotive haulage, not least their probable technical improvement. Given such a marginal judgement the directors of the company decided to hold a competition to test the locomotives on offer. Rastrick was one of three judges at the Rainhill Trials of 1829 which conclusively proved the benefits of the Stephenson 'Rocket' locomotive. Rastrick's diaries and notebook of the trial are valuable records of the performance of locomotives of that era.