Look at images of spider mite webs and compare with your issue. If you think it’s a match look up solutions to that pest..

However, these heathers are hardy outdoor plants of a temperate climate which are really not suited to indoor culture. To be honest you’ve done well to keep them going this long inside. If you don’t live in a climate suited to their needs it’s probably best to treat them as temporary decoration. Looking at the radiator I’m guessing you’re in the British Isles. If that’s the case they’d be happier outside in a container of ericaceous compost. They’re staples of winter containers. (Warning to USA readers.’Compost ‘ has two meanings over here, one of which is ‘mix.’)

Yes: cool climate outdoor plant lingering indoors = eventual mite infestation. With the time when these pests become noticeable outdoors being during the hottest and driest seasonal weather conditions, that are most like temperatures and humidity of inhabited indoor spaces.

If OP is in the British Isles spider mites will be pretty much unheard of on an outdoor heather. So the sooner it goes outside the better.