1. Encourage Ladybirds.

You can encourage ladybirds by providing suitable places for them to hibernated. You can buy ladybird boxes from specialist retailers.

2. Encourage Hoverflies.

Hoverflies are voracious eaters of greenflies. You will hopefully attract hoverfly without any effort. But, you can increase the hoverfly population by providing boxes to overwinter them. Geoff Hamilton used to encourage hoverfly and used to even harden off the hoverfly boxes like you would young saplings. It is also said that having a bunch of nettles encourages hoverfly because nettles provide an early season supply of aphids which encourage hoverfly populations for later greenfly infestations.
You can also encourage hoverfly through companion planting. E.g. Marigolds are said to attract hoverfly.

3. Hose off Aphids

You can use a power water spray to shake off aphids which have are eating off the leaves and buds. This will reduce most of the population, but, some are likely to survive. This is a good strategy if you are waiting for hoverflies to do their business.

4. Kill them with your fingers.

Not practical for large swathes of plants but if you have a prize rose, close inspection and killing off aphids with fingers can be an effective way to keep them clear of insects.

5. Organic Sprays.

If all else fails you can try an organic spray which can kill greenfly without breaching organic standards. Some tipsters recommend painting insects with methylated spirits but that seems contrary to organic practice.

• Organic Pest Sprays at Amazon

Related

• Tips for dealing with slugs and snails
• How to encourage wildlife in your garden
• Top ten Green Garden Habits

Organic Gardening by Geoff Hamilton
Covers many ideas about your own Organic Garden.