What about for services covered by enhanced partnerships where the local authority doesn’t support the service?
I think technically, they can, but it's a fairly recent power, and not sure it's actually been used yet.
TC's can of course refuse the 'short notice' element of a change if they don't think there's a good enough reason for the short notice, and insist on the 'proper' notice period being given.
There are a few exceptional circumstances where TC could refuse an application if the local authority objects on road safety grounds (again I don't think it happens often) and there's also the power to restrict any new applications on the grounds that a particular bit of road already has quite enough buses for safety (I think that decision has to be made before any specific registration / variation is considered.) The latter is quite a rarity, and not sure quite what the process is for making a decision like that - I'm only aware of a small handful of cases where this has happened since deregulation, and haven't personally been involved in any.
only if the information supplied is clearly wrong or incomplete
I've known applications refused (or at least sent back with a 'try again') where the proposed timetable in some way doesn't meet the legal standards, e.g. frequency and running time will vary depending on what the traffic's like that day (I've known an operator try that in a seaside town), or where the timetable doesn't meet the standards for a local bus service in some way, e.g. very long distance / time gap and vague route details between two timing points.
But the centralised office for registrations don't have any sort of local knowledge so things can get through if they are just not clearly wrong. From a local authority perspective, I've had registrations where the route map and written route description don't match, and in one case, with a timing point in the timetable that was not on either, and then there's ones where the running time is very wrong one way or another.