contractual obligation

Transport Ian takes a Parliamentary train journey. It's not what you'd think:

"A mysterious train runs between North and South London during the week, direct between two stations that shouldn’t be possible to travel between. Once in the morning, and once in the afternoon – and never at weekends.

From Wandsworth Road to Kensington Olympia – this is London’s Parliamentary Train Service.

It doesn’t exist to serve our elected masters in Parliament, nor is it required due to some little known outpost of the Palace of Westminster in Wandsworth – it is in fact a relic, a remnant that exists simply because of a strange bit of legislation passed by Parliament."

I'm genuinely interested. There are some buses in Liverpool that only travel once a week, often very early on a Sunday morning. Are they a similar contractual obligation?