From where you live it sounds logical to use A1, M11 and Dartford crossing but I bet if you measure both routes there might not be a lot of difference. Road works might sway your decision.
Personally I prefer to travel round the Heathrow side of the M25 when I go North and back again - I just don't like the motorway on the other side but that might have something to do with where I've lived in and around London than anything else. It always seems to flow pretty well.
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In the past we have gone via Dartford crossing when heading to Folkestone/Dover. Distance to Newhaven is round about the same either way, was thinking more about the volume of traffic bearing in mind it will be late afternoon / early evening on a Saturday.
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This is a run I do regularly, starting on the A1 through Lincolnshire.
There is only just about 2 miles difference in it, and now the M25 4-lane round the East side to Dartford has been finished, the A1/A14/M11/M25 is the better route. The M1 still has roadworks from J13 down to J10, and the M40/M4/Heathrow stretch can be busy.
However, it all depends what time you think you'll be at the Water Jump. That said, Saturdays are not usually any problem. Just keep your ears on Radio 2's traffic reports in case of jams or accidents on the bit you want to use, and be prepared to change.
The best way from the M25 to Newhaven is via the M23/A23 past Gatwick to Brighton and then the A27 to Lewes (all dual as far as Lewes). The A22/A26 from M25 J5 is OK but slow through Royal Tunbridge Wells and onward. The A22 from J6 is a definite "no".