This sounds like something dumb that I would do, though I would be traveling from Crewe initially. None of the Traveline sites are offering me the journey (any operator, bus only), so any ideas on an itinerary to try and do it would be appreciated.
Seeing the £10.50 Stagecoach NorthWest Explorer ticket mentioned earlier, I was intrigued by how feasible it might be to do the full trip in one day and the answer is not too difficult (if you like buses).
Here's an itinerary from Chester to Newcastle-upon-Tyne that's not too early a start, not too late a finish and long enough connections to reduce risk of missing one and for toilet stops etc.
[xx] indicates the bus route number.
08:45 Chester Bus Exchange [X8] Liverpool Whitechapel arr 09:55 *
10:06 Liverpool Queen Sq [X2-2X] Preston Bus Stn 12:06
12:30 Preston Bus Stn [40] Lancaster Bus Stn 13:47
14:20 Lancaster Bus Stn [555] Keswick Bus Stn 17:02
17:40 Keswick Bus Stn [554] Carlisle Bus Stn 18:50
19:07 Carlisle Bus Stn [685] Newcastle Eldon Sq 21.18
* If you think the Limited Stop X8 is somehow cheating, or don't fancy the +11 connection in Liverpool, you could start from Chester on Service 1 at 08:05, which has a "+18" in The' Pool.
If it's a nice day, you could set off about an hour earlier and break the 555 leg somewhere in the Lake District (Ambleside, Grasmere or some quieter spot) and pick up the next 555 an hour later.
The last leg on the 685 is an Arriva bus, but Stagecoach tickets are valid.
You arrive in Newcastle in plenty time for a celebratory pint of their Brown ale.
Coming back south, I'm not sure if it's possible. The 685 Newcastle/Carlisle is jointly operated by Stagecoach and Arriva, and you'd need to wait for the first departure from Newcastle operated by a Stagecoach bus which is at 08:45. Although you can use the NorthWest Explorer on the 685, you cannot buy the ticket on an Arriva bus.
So it may be the train home at £69.50 Anytime Single (or pay Arriva for a single to Carlisle on an earlier bus).
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Again straying into the realms of day rovers, but a £10.50 Stagecoach North West day explorer will (in theory) get you from just over the Welsh border in Saltney (near Chester) to Newcastle on Tyne or Dumfries.
There are some epic treks possible by stage-carriage bus using a Stagecoach Northwest Explorer and tacking an additional trip on the end.
With a start around 6 to 6.30am and finishing around 8 to 9pm you can squeeze the value out of your ticket by doing Liverpool/Manchester to Edinburgh or Glasgow via Preston, The Lakes and Dumfries for around £20 (after adding the extra fare onwards from Dumfries).
It's Stagecoach companies all the way if you start from Liverpool.
Starting from Manchester, you now need to pay First Manchester for the ride into Bolton, since Stagecoach withdrew the historic X60 Manchester-Preston-Blackpool service.
Not for the faint-hearted, though.