If your telly is plugged in, with an aerial connected to it, it's "installed" (which is what the legislation refers to) and you need a licence even if you never turn it on.
Assuming that you're using Freeview (rather than, say, Sky), if you've lost the main BBC channels then (assumining that there's not a transmitter fault), the signal strength is insufficient for your TV to 'lock onto' the frequency used by the PSB1 multiplex. Get one of these
https://www.argos.co.uk/product/9383027 , one of these
https://www.screwfix.com/p/fly-lead-coaxial-plug-to-plug-1m/41720 , install them, rescan and your problem should disappear).
You can check for transmitter problems here:
https://ukfree.tv/maps/live
(Zoom into your area. Hover your mousecursor over the relevant transmitter)
Alternative site:
https://www.bbc.co.uk/reception/check-for-transmitter-faults/#/undefined