He may well have struggled in other subjects as you imply, though I would have thought the handwriting was from several years before.
The handwritten diary type text mentions Sunday May 6th. In 2007 May 6th was a Sunday.
I don't think he was being bullied, he had a 100% attendance record at school.
According to comments in the below video, the cheap return ticket price was only valid for the day.
Knowing how much the one way ticket cost, would ascertain how much money he needed for the return trip.
https://www.youtube.com/watch?v=N2xAsREdRTcIn the above video Andrew's bedroom is featured. There's a glass cabinet of attractively displayed rocks.
With his relatives living in Sidcup & Chiselhurst he may have often visited the nearby caves, piquing an interest in Geology.
In the below video someone traces what could have possibly been Andrew's walking route, around Central London that day.
https://www.youtube.com/watch?v=Us06yXKfGeIWith a possible final destination point of Charring Cross Station, where trains depart for Sidcup and Chiselhurst (caves) .
I think Andrew did intend to return home and was simply making a spur of the moment decision to visit the rellies.
A child each way fare from Doncaster to London and back would have still left him enough money over.
He simply left the 100 pounds at home so that he wouldn't blow all his money on the one trip.