As a general rule, avoid buying single tickets wherever possible! For triangular journeys it's usually cheapest to retrace your routes by buying A-B and B-C returns rather than A-B, B-C and C-A singles (obviously this can take longer).
However, in this case a London-Edinburgh Super Off Peak Return (£121.40) would be valid for your plans. Stop "short" at Newcastle on the outward (permitted for this ticket), then on day 2 travel Newcastle-Crewe*, break journey (always permitted on the return part of tickets), day 3 direct Crewe-London.
*You're limited to routes which can be traced on
map AS of the Routeing Guide from Edinburgh to London without retracing your line at any point. That means you can't go Newcastle-Carlisle-Crewe, nor can you travel via Huddersfield. The best route seems to be Newcastle-Sheffield, Sheffield-Stockport, Stockport-Crewe.
The time restrictions which apply to this ticket are described in the code
9F; it's valid on any train except those which are specifically excluded. It's fine for your itinerary.