comeflymark - Several operators do however, impose their own Company speed limits on departure in order to ensure that aircraft maintain the correct SID lateral profile where there is a large turn after take-off e.g. Gatwick westerly DVR SIDs and Luton easterly CPT SIDs.
Irrespective of the instruction "No ATC speed restriction" it's up to the flight deck to ensure that they follow the SID lateral profile due to the close interaction of many LTMA SIDs.
The 4000 feet restriction to which you refer is probably the Noise Preferential Route (NPR) altitude ceiling above which ATC can legitimately radar vector you off the SID (all LTMA SIDs incorporate the applicable NPRs). This has nothing to do with SID speed limits.
