I agree the sentence with "this" means the visit is still in progress. I wouldn't say the sentence with "that" is wrong. Using "that" would imply more distance and that she is telling about her visit which is no longer in progress.
1. So, it sounds like you enjoyed yourself. Was that your first visit to England? Yes. That was my first visit to England. (That's the first time I was in England)
1. She said that was her first visit to England.
2. So, how long will you be in England? Is this your first visit to England? Yes, it is. This is my first visit to England.
2. She told me this was her first visit to England and that she'll be here for another week. She said this was her first visit to England. (This is the first time I have been in England.)
Note For Number 2:
It would seem odd to use "was" while the visit is still in progress, but it does not strike me as being wrong.
If we use "this" I think it is better written as follows: She said this is her first visit to England.
Using "was" wouldn't be wrong, though it would be lacking in logic to some extent if the visit is still in progress. In any event, I'm sure many people would be apt to say in that way.
I hope I haven't confused you more, but this is how I see it.
I imagine someone will post a briefer answer if this is too much.