List of approved professional associations?

Pennywise

The "approved" list of organisations etc is for the employed only - in HMRC's employment manual.

There is no such list for the self employed where the rules of tax allowability are different. For s/e the basic rule is whether a payment is "wholly and exclusively" for business purposes. The ICO fee is without doubt allowable under this general rule as long as you need ICO registration as part of your business.