I always reckon that it takes between 3 and 5 days to get into ketosis on a VLCD. It very much depends on whether you have had a carb fest in the days running up to starting - I always try to cut down before I start one.
With regards to the milk, when you consider the Working Solution allows some skimmed milk AND a meal, and Cambridge SS+ also allows for milk, and you will still remain in ketosis, I should think that some milk wouldn't do too much harm, although if you could avoid it until you are in ketosis, that may speed up the process.
Having said all that, I am no expert! That is just some logical guessing I'm afraid!