There don't appear to be any systemics in the advisory below:
(Not that I'd be picking off leaves)
No - but that is an American site and says that sulphur sprays and a tar wash are acceptable "organic" standards. Not that I personally think they would be very effective, or acceptable to the uk Organic" Industry. !
Fortunately the problem is not mine, and the OP will have to make his own decision. You have my first line suggestion.
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It looks like the following are recommended by the trade.
Active ingredient Chlorpyriphos
IRAC code 1B
Formulations Dursban WG, Equity (Dow)
Action(s) A contact and ingested organophosphorus insecticide. Incompatible with biological controls.
Active ingredient Fatty acids
Formulation Savona (Koppert)
Action(s) Contact acting — destroys insect cuticle. Short-term effect on some biological controls.
Active ingredient Diflubenzuron
IRAC code 15
Formulation Dimilin Flo (Certis)
Action(s) Selective and persistent insecticide. Compatible with biological controls.
Active ingredient Spirodiclofen
Formulation Envidor (Bayer)
IRAC code 23
Action(s) Contact–acting insecticide. Incompatible with biological controls.
Active ingredient Lambda-cyhalothrin
Formulations Various including Hallmark WZT* (Syngenta)
IRAC code 3
Action(s) Fast-acting, persistent, contact and residual insecticide. Incompatible with biological controls.
Active ingredient Pyrethrins
IRAC code 3
Formulation Pyrethrum 5EC (Agropharm), Spruzit (Certis)
Action(s) Contact insecticide with short-term effect on biological controls.
Active ingredient Petroleum oil
Formulation Spraying Oil (Certis)
Action(s) Insecticidal oil that acts by physical means. Incompatible with some biological controls.