Cherry Aphids- Organic Dilemma?

oh dear
Once the leaves have become curled it is too late for effective spraying. Do not spray during the open blossom period in order to protect bees.
Royal Horticultural Society - Gardening Advice: Cherry Blackfly

Preventing ants climbing up the tree (via a greaseband?) will allow aphid predators to attack without having to fight off swarms of ants. Aphid predators go elsewhere (to unguarded aphids), rather than fight hundreds of ants for every meal.
If you have any rose bushes (always a favourite of aphids) you may find some tiny yellow-orange "maggots" living among the aphids. They are hoverfly larvae and (after removing the ants) putting just one or two into each aphid colony ought to make the aphids completely disappear in a week or two.

I have just done my evening walk around the garden and have noticed some strange green flattened caterpillar-like creatures that seem to be eating aphids. Certainly there are fewer aphids left on the leaves where these rippling green things are. Any idea what my mystery green creatures are?

Edit: a bit of googling later has revealed them to be Syrphidae larvae:

HOVERFLIES (Diptera: Syrphidae)
So called because of the adults hovering flight, adults feed on pollen, nectar and honeydew, all are brightly coloured and often mimic bees and wasps. Larvae are predatory and Adult females lay one or two eggs near an aphid colony, these hatch in 2-3 days. Characterised by no legs or eyes and body shape tapers towards head where black arrow shaped mouthparts adapted for piercing aphids can be seen. Larvae usually feed at night, each individual may
consume up to 200 aphids and by the final moult reach 10 - 20 mm in length. First generation larvae feed May-June and there may be up to 3 generations per year. Considered to be important predators early in season.

Most interesting, I am off to pick a leaf get my magnifying glass and watch an aphid hunt!

Here is a website offering natural pest control, including pictures of the hoverfly larva, ladybird larva and parasictic wasps, so that you can see what your allies look like (scroll down the link).

Aphid predators

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I can report the tree has been nearly cleared of aphids: just the odd one or two remaining. The syrphidae larvae also seem to have gone too. I watched a few aphid hunts, the larvae are fearsome beasties and seem to rear up in triumph when they attack! Fascinating and educational. So no need to spray after all. Thanks everyone for the help.

Just like in the movies; the situation deteriorates to the point where it appears hopeless, then the cavalry arrives to save the day!