I will never forget the time _I spent with Tom travelling around UK

that也行啊~~~~~定语从句~~~~~~~

which,是不是翻译成:我将永远不会忘记我与TOM旅游英国的时光.
这里的the time which I spent是which I spent 修饰the time,是后置定语

你要这样看,我和TOM一起spent的是days，days作的是spent的宾语

因为the time是作为spend的宾语,也就是说,time在从句中充当的不是时间状语,而是宾语!所以要用which

which /that
是定语从句

the time解释成一次的话应该就可以通了