Just back from this ride. I don't think it is a standard route to Edinburgh but one I chose as I planned to stay with a friend in Hull. As it happened he had COVID so I could only wave at him.
Going this way does mean a trip over the North Yorkshire Moors. I thought the climbs were worth it for the experience and compensated for the flat of the Fens. Boston Lincs. and South Shields turned out to be unexpected gems.
My son and I did this in seven days, averaging around 80 miles a day, which turned out to be hard going for hobby/commuter cyclists, averaging 10-12 miles/hr. If you do not examine the route in grannular detail you will find unexpected areas of poor surface that will hit your average speed for the day. In two places we found Route 1 blocked by building works, in and near Middlesborough.
We had a short day when there turned out to be no accomodation of any kind in Whitby and we had to stay further down the coast. Not a problem anywhere else on this route.
If you are planning any route to Edinburgh the cycling along the coast in North Northumbia is amazing. Great tracks, well surfaced, next to the sea. In other places Route 1 is poorly surfaced. Particulary the Cinder Track from Scarborough to Whitby which in parts around Robin Hoods Bay is more like stream bed.
The climb to get over the hill from Berwick to Eyemouth is tough at the end of the day and needs to be repeated in part the next day but worth it for the long descents. Don't even contemplate using the A1.
Using the tunnel behind Arthur's Seat in Holyrood Park, part of Route 1, is an amazing way to enter the city. You emerge close to the centre and with no climb to the castle.
A big thank you to cycle.travel and it's route export function to Garmin without which I doubt we could of done this.