If you are coming from the North down the A1, you will be fine to get to Burghley normal route.
If you are coming from the South, you will need to come off at the A1139 Peterborough junction (Services at Haddon), then about 3 junctions down, take a left onto the next stretch of dual carriage way sign posted towards the A47. You can then join the A47 and get to Burghley via Southorpe and Barnack (all sign posted for Burghley any way.)
Luckily I spotted stationary traffic on the A1 and was able to nip off at the Barnack turn and go the cross country route home.
Local news and papers are saying that the A1 will NOT BE OPEN until at least midday tomorrow. They have put diversions in place but as there are really only 2 roads into Burghley it will mean there are long delays in every direction
Leave early and plan to leave late - the worst times for queues on a 'normal' Burghley saturday are between 9.30-11