I don't recall receiving the 2000'/min type clearances in the UK very often so I don't see how the UKAIP will help. This is a speciality of Germany and more recently Maastricht. Have you had this clearance in the UK? I can only remember it once towards Biggin when asked for 270kts, 2000'/min and level by Tiger.
Anyway as far as the general point goes this has been done before and the answer is that if the controller doesn't repeat the restriction of ,say, be level by Saber then the restriction no longer holds. That is the letter of the manual as I understand it. However, I have read here that while that may be technically correct it might actually be useful just to comply with it anyway in case the controller has not pedantically stuck to every T crossing and I dotting routine required.