In the UK, MATS Part 1, Section 1, Chapter 13 (page 189 of the link below) covers speed control. Can't find reference for rate of climb/descent.
https://publicapps.caa.co.uk/docs/33...il%202015).pdf
UK military controllers don't do speed control but MOD policy on climb/descent rates is that a normal rate of climb/descent is not more than 8000ft/min, a restriction that can be lifted by the controller if required, but we are not worried about G&T being spilt by the SLF.