I know at LHR, CFMU do not issue CTOT improvements no nearer than the present time + taxi time + Time to Insert into Seqce Time (TIS = 10mins at LHR).
So if time is 1000loc and dep 27R (20mins taxi time), the earliest improvement that could be issued would be 1000 + 20 + 10 = 1030loc!
Hope this helps.
Cheers!