Britain is currently commemorating 200 years of railways with a series of events having taken place this year, arising out of the 200th anniversary of the opening of the Stockton & Darlington Railway, which will occur on 27th September.
However, this was not the first railway in Britain/globally as many mineral tramways predated this. In addition, there was at least one passenger service that predated the S&DR, which was the Swansea & Mumbles Railway in Wales, also known as the Oystermouth Tramway.
The line was built to primarily carry limestone from Mumbles to Swansea, however, a horse drawn passenger service commenced in March 1807.
The BBC has an article going into the details.