Thanks scottishskifun - yes found them!
It seems that the "required distance" of 1m only applies to "a person who is responsible for a place of worship, carrying on a business or providing a service in a Level 0 area" rather than the public themselves, and that person only has to put in measures to ensure that distancing "as far as reasonably practicable" , including only allowing the number of people on/in to permit that. So I suppose LNER and Scotrail should be limiting people boarding their trains, even if they have a valid ticket, so they can each be 1m apart. Though if that would work with their other obligations (including keeping their staff safe!) and so be reasonably practicable, I don't know. It must be a nightmare for eg hospitality businesses who have the EHO obligations too, as well as awkward customers.
I suppose the police could get involved for breaches of social distancing when there were limits on gatherings (and I suppose there still are, if you have a house party with more than 8 people) but presumably not 2 people standing closer than 1m apart! Though that doesn't seem to be against the law anyway.
Re starrys point - yes, but I suppose that applies to anything! If you can't persuade people that something is a good idea to do/ not do purely through asking/ persuading them, then you can make it law, as people are less willing to break the law generally. Kind of using a stick if the carrot hasn't worked! Because there is a risk they could be fined, closed down, or even spoken to by the police about it - even if unlikely - which many people want to avoid (though as with all these things, the risk is probably greater if you are of certain demographics, or display certain behaviours than others). So I don't think it's purely "just a way of encouraging a certain behaviour" any more than any other law is!