if the same Mux is bad for all of them as you say, then the only option short of going up there and adding some form of higher gain arial or extensions, is a signal booster on the TV end of the coax, to compensate for the long feed lead signal loss.
that so called basket is your parabolic reflector on the "yagi" helping to concentrate the incoming radio waves on to the dipole feed, if its not evenly spaced to the other side, it MAY (or not) be concentrating the radio wave in slightly off center hence giving a slightly lower db gain that its rated for, the higher the gain on the arial the better and stanger the signal down your coax.
exactly the same idea as the wireless router DIY arials/reflectors booster text iv posted elsewere.....but tuned for the DVB freqs OC
basicly the more elements a Yagi arial has the higher its gain and the stronger it can pick up the signal from 40 miles away...
this ones got 15 elements plus the dipole at the end then the reflectors at the back concentrating the incoming signal on to the dipole with the black arial cover connected to it...
something i didnt realise until i looked too
each DVB-T element group is a different size
---------- Post added at 01:35 ---------- Previous post was at 01:31 ----------
if you wernt so far away you might have got away with a higher gain arial mounted in the loft were you could have easily got to it and adjusted it for best picture on the weakest analogue picture.
you do it that way so as to maximise for best digital reception without a meter to help you point it optimally.
you can still try that OC but at 40 miles its going to be more than borderline not being line of sight outside....
the booster seems like your probable best option, and it neednt be a great gain to bring the mux into signal strength, its usually eather in or out with digital reception and it sounds like its just outside that clear digital reception line right now....