Biff Vernon's site gives much of interest on the history of the GNR
No online, but Frank Goddard's book "the Great North Road" (pub Frances Lincoln) is a guide to the historic route, with mapping in the style of Wainright's Lakeland Fell series.
Much of the old Great North Road has been bypassed, but significant parts have not, notably Baldock to Alconbury, Peterborough to Newark, a few strectches in Yorkshire, notably Dishforth to Scotch Corner, and significant patrs in Northumberland and the Scottish borders. In places the new alignment has stopped up the old, making it impossible to follow in its entirety without backtracking.
The traditional start of the GNR is not actually Smithfield but St Martin le Grand - the original site of the London General Post Office - the other end is its Edinburgh equivalent. I surmise that the "totso" at Angel is because, even in the days of horses, mail coaches were easier to steer than meatstock being delivered on the hoof to Smithfield.
The approximate route of the GNR, according to Goddard's book, follows the A1 to Highgate and then the A1000 all the way to Hatfield, where it follows two culs de sac linked by a footbridge over the East Coast Main railway Line (not clear from Google Street view whether you could wheel a moped over it, but it is part of the national cycle network), before briefly folloing the A414 and A6129 to Welwyn and then the B197 most of the way to Baldock (give or take a pedestrianised bit in Stevenage)and the A507 to join the A1 at the end of the motorway section.
It follows the A1 from there all the way to Alconbury, except where the A1 bypasses Biggleswade (A6001), Tempsford (unclassified) and Eaton Socon (B1428 and unclassified). From Alconbury the B1043 runs next to the A1(M) both following the GNR/Ermine Street, except that they both bypass Stilton. Beyond Norman Cross there is a short stretch of motorway with no obvious alternative before the A1 resumes, and the GNR follows it most of the way to Newark except through Stamford (B1081), Grantham (B1174), and Long Bennington (u/c).
From newark the GNR and A1 are rarely the same, the GNR following the B6326 and B6325 through Newark, B1164 to Tuxford and Markham Moor, A638 through Bawtry and Doncaster (partly pedestrianised in the town centre) to the top of the Doncaster bypass. You're then on the A1 except for the Wentbridge bypass until you reach the motoprway - the old GNR runs very close, mainly as the A162 but that itself bypasses the old bridge at Ferrybridge, then the A1246 and then unclassified through Micklefield and Aberford. Beynond Bramham you're back on the A1 as far as Wetherby, and then A168 paralle to the motorway, with brief detours round places like Leeming, all the way to Dishforth. From there to Scotch Corner you have the roadworks as the road is being convreted to motorway, with a new all purse road alongside, but after Scotch Corner the A167 is your friend all the way to Newcastle (brief departure in the city of Durham). North of the Tyne you have A189 and B1318 to Seaton Burn, a brief section of a1, then the A197 and A192 through Morpeth. Beyond there it's largely A1 except the B6341 through Alnwick and the A1167 through Berwick. Between Burnmouth and Cockburnspath the A1 is well established, butb the original route is apparently the A1107. finally, The A1 bypasses Dunbar, and a long stertch where the A199 follows the old route.
) and one thing I would like to do is travel from Smithfield Market to Edinburgh using the great north road.
