On arriving in England, they were taken to the Crystal Palace by train.

On是介词, 后面跟的动词要变为动名词形式.

因为arrive是在介词on后面，所以必须变为动名词形式arriving.

on doing sth
一到***地方就做某事，壮语丛句

因为在它前面是介词on,on/upon 有“当什么时候”的意思，它后面是需要ing形式的。