If you are traveling from Newcastle to Glasgow you should be fine.
I'll let you into a little secret.
There is a vehicle called a DVT, or a Driving Van Trailer at one end of the Electric trains, Intercity 225 or the class 91 hauled/propelled trains.
If you are travelling North, then the DVT will almost always be at the very back (London End) past the First Class section. Walk down and ask to put your bikes in there. It's simply an EMPTY coach!!
I always dump my heavy luggage in there when I travel up from London so I don't have to bother about it (you don't have to be a first class passenger either). You only have to ask and they should be willing to do it for you as most people do not even know the space exists so the humble DVT's capacity tends to be grossly underused.
It is the empty bit between where the train guard sits and where the Driver's cab is, so it's secure, and as I say, most people do not even know it's there, partly because it looks the same as the loco at the other end, except that it's not a loco, it's a driving trailer. It's past the First class section too, so you don't get much riff raff in that bit of the train.
Having said that, I'm not sure if it has cycle racks, so you might have to leave them on the floor, I'm not sure as I have only ever used them for luggage (I leave my bags under the metal table usually). I think there are things for securing items though. It might be useful to try and enquire about that, but certainly, the trains DO have the space, so I'd advise you seriously to ask about it.
The DVTs are the ones with the big sliding side door.
I don't know what circumstances would prohibit it's use as I have never encountered any problems with it before (other than once when I was going from London to Glasgow and they had brought my luggage out at about Carstairs without me knowing, so it was sitting there outside the guard's van in the vestibule of the first class coach instead!).
No, you don't have to hire a car, just ask for the DVT.
You will not get a DVT north of Edinburgh though as the Inverness and Aberdeen routes are worked by HSTs, or Intercity 125s to the layman.