Following sentence is right:
Not only did she go to London but she also visited many other places in England.
This sentence is incorrect because "Not only she went...." means " Not only she alone went.......". Compare it to:-
"Not only she went to London but her boyfriend went too."
If you want to use went, the sentence will have to be changed to,
"She not only went to London but also visited many other places in England."
It is because you put a negative phrase "not only" at the head of your sentence. If you didn't so, the sentence should be : "She not only went to London but also visited many other places in England". The rule that we have to invert the positions of the subject and the verb when we put a negative phrases at a sentential head is called "negative inversion". This rule is a bit tough to acquire for learners whose mother tongue is not the one belonging to European languages. But the acquisition is very important, because , in some cases, if you don’t do the subject-verb inversion, the meaning turns to be totally different from the one where the subject and the verb are inverted. For example, please compare:
(1) Not even two years ago(,) I did love her.
(2) Not even two years ago did I love her.
Native speakers take the sentence #1 as saying "It is not even two years ago when I did love her". That is, the sentence means "I loved her even less than two years ago". The sentence #2, on the other hand, is saying "I didn’t love her even two years ago".
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