I noticed that in England they use the form 'have done' more than the form 'did do'
ie: 'Have you talked to him again this week' instead of 'did you talk to him again this week'
What is the difference between the two tenses and If I'm talking in British english which one shall I use?
The basic distinction is the association with now for the present perfect. In the example you give,m there's an unfinished time period, so the visiting status could change later on in the week. If you asked about last week, where there is no possibility of changing things, then 'did you visit' would be the choice.