You're phone isn't using power by having an unused internet service available through phone masts. You can't turn that signal off without rendering your phone unusable for incoming and outgoing calls, as it's the same one that's used both for calls and for connecting to the internet.
However if your phone is constantly looking for a wi-fi connection from, say, your home router, then it will be unnecessarily using some power. So, in your circumstances, it would be best to turn the wi-fi off. If you don't know how to do that, Section 5 (on page 16 here) should help:
https://www.imomobile.co.uk/wp-content/uploads/2018/08/IMO-Q2-Plus-User-Manual-v2.pdf
(That's the manual for the Q2 Plus, rather than the Q2, but it's likely to be the same. Alternatively, most Android phones allow you to enable/disable wi-fi by pulling down from the top of the screen and tapping the relevant button).