The OP - and the following posts in support of the First Class passenger - especially ymb's
//I stopped using first class when they continually allowed scum into the carriage. //
demonstrate admirably that the last bastion of in-built class snobbery and unfounded superiority lies firmly in the 'class' system of train travel.
If I buy a First Class seat on a train, it allows me to travel in First Class.
Nowhere on the Terms and Conditions does it confer on me the right to make an arbitrary decision about the suitability of others who may share the carriage with me.
And amen to that! You'd have people objecting to passengers who were not wearing a suit, or who had on trainers not spats - where on earth do you draw the ludicrous small-minded petty snobbish selfish line?
If I was seated in a First Class carriage and any passenger of any age, social status, and parent status sat next to me, I would not consider it my right to start objecting to their presence - it is not my business how the train company allocates its seats.
But - if a tired harassed and grateful mum with a happy baby sat next to me, I would be happy to have a chat with her about her little one, not be offering her a lesson in civics which she did not ask for and does not need.
Had I been a witness, I would have offered my seat to the young mother, as did the kind gentleman in the carriage.
The ignorant, arrogant snobbish chippy baggage of a woman who caused the fuss should be utterly ashamed of herself.