It look like it could have been be an Orange/T-Mobile single band site. Looks to be pretty much the same as the Alifabs Styrosun on Peter's site halfway down
Compact Monopole and Streetworks masts used for EE and 3 UK Mobile telecommunications in the United Kingdom
pedroc.co.uk
Top middle, just without the MW dish:
If it's no-longer there then I'd think it probably got consolidated when they merged and they chose the better of the two sites near eachother to keep (the taller/higher lattice on the top of the hill), or that was done when MBNL redeveloped the site (and moved to the lattice then).
I don't think there'd be a way to know which provider (Orange or TM) the site was for now that it's been removed.
Looking on cellmapper it seems that both EE and Three sites have been positioned on that monopole but their coverage polygons suggest that they should be positioned at the lattice just to the south.
If your other site says T-Mobile then that one sounds like it would have originally been that, but will now be EE (with, or without Three, depending if there's been significant changes to it).