Just in case TUPE doesn't mean a lot, more (ACAS website) about it
here.
I've been on the receiving end of TUPE (not on the railways) a couple of times. Just to add some of what's above, it's not a case of 'invited' to transfer, if an 'economic entity' (such as a train franchise) changes hands, then the existing staff who work mainly or wholly on that activity get to transfer across on existing pay and conditions - and length of service for things like redundancy pay and protection from unfair dismissal is counted from day one with old employer - you don't start from day one with new employer, and they can't impose a new 6 month probationary period or anything like that (they tried to do that with me on one occasion...)
Broadly speaking, all existing staff in the relevant job grades are eligible to transfer.
New employer can't pick and choose who to take on (and in some cases can end up getting staff back who they have dismissed before - and they can't re-sack someone for the old offence. A bus company I used to work for got one driver back about 3 times following take-overs and had to catch him fiddling and sack him again each time)
Old employer can (but does not have to) offer alternative employment to all staff eligible for transfer (this probably isn't practical in the case of a train franchise changing hands - although they might offer transfers to other bits within the group if it's that sort of operator)
they also can't pick and choose who to keep on (unless it's by open applications for a different role) - if this happens, it's up to each employee whether to stay or go.
And you can't decline to transfer and claim redundancy, it would be resignation if you refused to go. (as with anything, there can be exceptions - if new operator was planning to run everything from a base 100 miles away, that might become a redundancy situation)
I would have thought train drivers are pretty secure in the event of franchise changes. Guards (or whatever they are called locally) and station staff possibly less so in the longer term.
And more complicated for people at PLC 'group' level whose job involves doing stuff for multiple of that group's franchises - they would probably not be eligible for TUPE.
(all of the above subject to the disclaimer that i'm not a lawyer.)
also, bear in mind that TUPE came out of European Law. Current government says it will put all existing EU employment protection law in to new UK laws, but as far as I know, hasn't yet done so.