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In the UK a lot of infrastructure (e.g. energy, fixed-line telecommunications, railways) is run by for-profit companies that are heavily regulated by the governmentWith the exception of HS1/Channel Tunnel, the vast majority of the UK's fixed rail infrastructure (stations, tracks, land, etc) is publicly owned.
The train operating companies (TOCs) are, with some exceptions, privately owned. But because of the way they are franchised and regulated there is little competition between them, so it's quite different to the electricity or internet markets.
> taking internet as an example, if you use the common infrastructure the speed you can get will be the same from all providers
Not necessarily. Although each provider may share a common "last mile" infrastructure, ie the lines that run to your house, they must each arrange their own equipment and backhaul in the local exchange where that line terminates. Not all backhauls are equal and some providers perform better than others, especially at peak times.
> Maybe electricity is a better example, as the electrons you receive will be exactly the same no matter which provider you use.
Every unit of electricity you use has to be generated somewhere - and not all sources are equal. As a consumer, I might place a premium on low-carbon electricity, and choose a provider which promises to purchase only from wind turbines and other low-carbon sources.