This was obviously harder than I thought. Without context it is pretty hard to get it.
Did she walk right into a wall, making it obvious to people that she expected to be able to pass through it?
Not a wall.
They went on a school outing to the tower of London.
But the Crazy Gang had taken it over
'orf with her head they shouted at Kitty
Fortunately her phasing power worked, avoiding the blow, but cluing in her school chums.
Ha! The Crazy Gang were not involved - this time!
Not - precisely - a school outing - or at least not an officially condoned one anyway.
The school, which was a girl's school only, was in financial difficulties so this bunch decided to do something to raise some funds. What might teenage school girls do - legally - to earn some cash? Hint: this involves a traditional school activity for teenage girls
particularly in the USA. Not sure if it happens in the UK, it doesn't in Australia, but then the writer was American.