Came across this when I tried to book my train ticket and a pleasant surprise to see only £4 for a single train ticket from Birmingham (New street or International) - Edinburgh Waverley (or Edinburgh - Birmingham).
The typical route is as follow but not all trains stop at every station so please check before you book the ticket.
Birmingham International Airport
Birmingham New Street
Prices as follow:
VALUE ADVANCE SINGLE C - £4.00 or £2.65 (with rail card)
VALUE ADVANCE SINGLE B - £5.00 or £3.30 (with rail card)
VALUE ADVANCE SINGLE A - £6.50 or £4.30 (with rail card)
VALUE ADVANCE 1ST SINGLE C - £10.50 or £6.95 (with rail card)
VALUE ADVANCE 1ST SINGLE B - £11.50 or £7.60 (with rail card)
VALUE ADVANCE 1ST SINGLE A - £12.50 or £8.25 (with rail card)
The price only comes out when you put Birmingham as starting station and Edinburgh as ending station, or vice versa, but if you try to search for Birmingham - Newcastle the price would be much higher. It's still a good price if you wish to alight at the intermediate stops, for example from Birmingham/Edinburgh to Newcastle/Durham/York/Leeds/Sheffield etc.
Personally I booked myself a 1st Class ticket (with railcard) at £8.25 - can't be better for a 5-hr+ trip!
This works on week days too,I just booked a Wednesday too.....brill offer.