And your first link said:
Until this change comes into force, anyone undertaking vehicle immobilisation activity must ensure that they are properly licensed to do so. Holders of an SIA Vehicle Immobiliser licence that expires before this time must either:

Cease this activity on expiry of the licence; or
Renew the licence if they wish to undertake vehicle immobilisation in England and Wales until October.

i.e. a license to clamp was only a stop-gap measure until October.