今天写了篇作文，要求如下

假设你是李华,上个月去英国参加了一次夏令营活动,活动期间一直住在Mr. Smith家中。他们给你提供了很多帮助,请写一封感谢信表达对他们的感谢

有一段我是这样写的

When I left China for the summer camp in UK,I began to worry about the difficulties I would have to face,but my worries all went away as you came to me,promising to make me feel at home as you can,and that was actually what you had done: you'd taught me the customs of UK so I wouldn't be embarrassed，you'd ……(后面是一串的过去完成时）

请问这里的时态用的对吗？另外，UK前有加定冠词the，也有不加的，它们之间有什么区别？