Globally,
Can't comment on the EGSS specific stuff, but the speed restriction is primarily there for ATC separation purposes during the early stages of the flight.
If there are no separation isues from preceeding traffic the speed restriction can be lifted with the phrase "no ATC speed restriction".
This releases you from the 250kts below 10,000ft restriction but it doesn't mean you must then accelerate. Although most do go faster when the speed restriction is lifted it is not a requirement, you can fly at whatever speed you think appropriate until such time as you're happy to go faster.
So if you're released from the speed restriction but think going quicker will make track keeping more difficult, don't accelerate until you're sure you're not going to have any problems.
HTH.
WF.