Hello, recently one of my fukien tea trees has developed a white, "speckled" spots on the leaves with weak, brittle leaves following after. I have read this may be honey dew or a mealy big infestation. However, I havent seen any bugs on either of the trees. I had to bring them both in due to an impending freeze and my other tree seemed to develop the same pathology shortly after, indicating it had spread due to close proximity. 

I have attached images below , any help would be greatly appreciated. Thank you.    

Have you checked under the leaves? Mealy bug are easy to see, It looks like an insect infestation, possibly White Fly. It is looking very bad so you need to do something now if not sooner. It is going to lose all the leaves by the look of it. I would spray with a WEAK solution of washing up liquid, one or two drops in a litre of water.

I found some yellow strips on Amazon that attracted white flies and stuck them. That fixed a similar problem I had. 
 

Yes, I looked last night and couldn't see anything. 

Just sprayed with a diluted washing solution. How often do you recommend doing this?

Once should be enough, wait and see