Despite the fact you haven't found any insects (they may have moved on up the tree to the young shoots by now, as is their modus operandi), I'm fairly sure this is apple woolly aphid, a very common but not too serious pest of apple trees. You can brush them off with a stiff brush, but if they have already moved to the tips of the branches, that won't do much and you may need to spray.
RHS advice on control:
From the pics it looks like woolly aphids. They are well hidden in the waxy cotton wool type coating which is very effective at protecting them from insecticides.
Google the term for some pictures. If it is what you have I suggest an afternoon with a bucket of soapy water and a nail brush scrubbing them off. You probably won't get them all (esp if it's a big tree) but you can control them in this way & they shouldn't affect the harvest too much. Many gardeners just try to keep these under control rather than full eradication.
Oops sorry Bob - your post sneaked in whilst I was writing - glad we agree...
Hi Sara, Best to avoid spraying at all if you can as it will kill the good bugs as well as the bad. The trick is to catch them early - as soon as you see a bit of the white stuff appearing next spring, get the scrubbing brush out! If it's a really bad infestation then spraying about the beginning of June would probably be best. You can also consider using a Winter tree wash when the tree is dormant which will kill the overwintering ones. That is less damaging to the environment than spraying when in leaf.