"Они собираются жить в Англии, а я не собираюсь."
Translation:They are going to live in England but I am not going to.
"Они собираются" can be translated as both "They are going to" and "They are planning to".
if you omit "to" the sentence makes no sense. "To" references the action stated at the beginning of the sentence, to -> live in England.
When dealing with things like this, just pretend the whole verb is "going to." It is perfectly fine to do this in many languages, because the concept of the word is syntactically different from its English counterpart. You could pretend it's "gonna" but if you don't like the terminating included preposition, you're not gonna like that word, either. We 'sophisticated' English speakers like to split our verbs into pieces to conform to other ridiculous rules. "to look for" becomes the clumsy "for which to look" and "to put up with" becomes "up with which to put." Why? Because someone in the past decided the language they stole it from was "doing it wrong" and it must be amended. Many of these translations are only clumsy and unnatural because English is a broken and VERY limited language. We may have a lot of words, but those rules...
While sometimes DL wants us to translate the intent of the sentence, it seems that in this instance, our job is to actually translate the wording of the sentence. The going to/planning to verb requires inclusion, it would seem.