They have always been capable of running above 100mph but there was an issue running in multiple with pan bounce on trailing set and a software glitch restricted them to 50% power using speed set in multiple.
The pan bounce is because the OLE isn't tensioned sufficiently for twin pantograph 110mph running, and because the pantograph used by the Class 350 is the budget version of the BR/BW High Speed Pantograph.
Performance would be significantly improved by swapping out the existing pantograph and fitting the deluxe model - that's the one with the aerofoils located underneath the pantograph head, rather than the one with the aerofoils on the knuckle.
The deluxe version does a very good job of keeping the carbon pretty much glued to the contact wire, the budget version does a decent job of keeping the pantograph head in roughly the right place but does little to stop bouncing, where the upper pantograph body and head rises and falls on the knuckle joint.
I never really did understand why BR and BW developed the lower spec version, really, there's not much difference in cost, just marginally lower carbon wear, I believe, at higher speeds.