There are competing operators in various places in Europe, the UK included. The clearest example is probably Hamburg-Köln-Express in Germany, which operates tr

There are competing operators in various places in Europe, the UK included. The clearest example is probably Hamburg-Köln-Express in Germany, which operates trains that take around the same time as the state-owned incumbent (DB Fernverkehr), but on older rolling stock for a lower price. The hard part is "how do you divide up the capacity on the infrastructure", but this is a problem that has clearly existed throughout the EU since 2007 (when there's been open access freight operators), though has in reality existed much longer (most international services, for example) hence track access and allocation being the subject of an EU directive all the way back in 1995.