You can risk the M1 if you like, but NO WAY would I. My daughter got stuck mid afternoon last week on the way South as she missed the turn across to the M40 and decided to risk it and it cost her over two hours!
If you are coming from the north take JNC 15A at Northampton services onto A43 past Towcester , Silverstone and Brackley to the M40 and Cherwell Valley services. M40 to M25 and around the south to JNC5 the M26 and onto M20 to Dover. 99 % of the time the A43 route is quicker than the M1 even when there are no roadworks! It is about 5 miles further to the M40/M25 JNC but well worth it in time and peace of mind and lower stress levels.
If the M40 has any problems you can cut down to the M4 on the A34 or past Henley say and you will not lose much time. Even the southern M25 you can easily re route from if there is a hold up. Problems around the M11 to the north and cutting off into north London if you have a problem are not so clever.
Bon Route ;-)