I live in London. Buses can get pretty wibbly wobbly, so it's best for kids to sit down. I've stood up to let a child have my seat before, and sometimes people have stood up and offered their seats to my kids.
Londoners can come across as a bit inconsiderate, but if you actually ask for what you want, they will nearly always help.
When I want to sit on a seat with a bag on it, I usually ask "can I sit there please?" and I've never had anyone who hasn't moved their bag for me.
When I've been pregnant and needed a seat I asked the person sitting in the priority seat "excuse me, do you need this seat?" - said in a genuine tone of voice, rather than a haughty one. Most people would then move for me, and occasionally someone would say "yes, I do", which was absolutely fine, because they needed the seat. It helped that I tended to look pregnant, but you can ask TfL for a badge if your pregnancy/disability isn't obvious.
Similarly, when I've been in dire straits and needed to haul a toddler in a buggy up a staircase, while simultaneously carrying a baby in a sling and a big bag or something. I'd give the odds of someone offering a hand at maybe 1 in 4, but if you asked someone for help, then about 4 out of 5 would.