This has been the case for so long that the 'ty' form is almost forgotten.
What are you talking about?
The common use of thee/thou/thine/etc. went out centuries ago! Yes, there are some vestiges of it in some Northern dialects (I'll si' thi' later) - but this is dialect.
I really don't think one can say that there is a familiar or singular form of 'thee/thou' in Modern English - that is just misleading. If so we would teach 'I - thee/thou - he/she/it' ... come on : )
Both examples were very posh English middle-class type people, who obviously have been educated a certain way, in a certain culture who in their minds think they are very refined people.
Hmm ... sorry, but going through your description, I can't see the rudeness. Now you know what that means? It means that in the cultural code in which those people have been brought up, they weren't being rude - so they weren't being rude. In the same way that if a Polish person is very direct with me, I can't take it as rudeness, because that is not their intention, so you shouldn't read the behaviour of these Brits as rude.
The old lady wasn't being patronising. If it was cold, and there were only three seats, and you were sitting in the middle, and are a man, and they are old ladies ... well, even as a younger woman I would straight away jump up and move over so they could sit down. To my mind, that you had to think about it was a tad ... rude. They were old, and cold too. Even if they hadn't been ... but usually the older female is offered respect and help.
When you did finally move, she was grateful, and thanked you - and in our language, she wasn't being effusive - that is just how we talk.
Actually she was rather polite, because she didn't ASK you to move - she just waited to see if you would. And that is another thing - we have an unspoken code of behaviour. The done thing would be to move. If you hadn't have moved, she wouldn't have asked - because it is your moral responsibility, your conscience, and she is well-brought up enough not to ask.
Again, two girls together on a train. You have your bag under a fold up seat, so effectively parked in that space. It is totally normal and not in any way rude for someone to say 'sorry - would you mind moving your bag?' - she was saying this because she didn't want to barge in, pull down the seat and possibly trample on your bag - and she also probably waited because she was checking that you really had just put the bag there, and not that you were in some way using the seat.
I just can't see the rudeness in either of these situations ...
And as for the language, what you might see as exaggerated politeness, etc, is just the way we speak. If you don't adopt that, you will always seem slightly rude/foreign ...
Genuine rudeness to me is, for example:
I have been standing in a queue at the post office in Poland for c. 30 minutes. We are all bundled up in layers of clothes as it is minus 20 outside, but the post office is boiling hot - only people keep opening the door, and then it is momentarily freezing cold. It is very uncomfortable in the queue. I get to the front, and just as I go to move forwards, an old woman digs me in the ribs with her elbow, and stomps on my foot as she pushes past me. She doesn't apologise, either, and she just carries on with her business.
Just tell me how that isn't rude ...