B757 FO REPORTS EXCEEDING 3000 FT AS REQUIRED BY SAM 3P DEPARTING EGKK.

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WHILE DEPARTING FROM EGKK ARPT RWY 8R; CLRED THE SAM 3P SID (SOUTH HAMPTON); WHICH REQUIRES A TURN AT 3 DME AFTER TKOF. THE DEP HAS AN ALT RESTR OF 2500-3000 FT AT D26DCT ON SID. FMS SHOWED SLIGHT MAP SHIFT TO N ON INITIAL CLBOUT. WE SWITCHED TO HDG MODE TO WAIT FOR 3 DME POINT FOR TURN. I; THE FO; WAS FLYING BY HAND. DURING TURN; FMS DUMPED ALT RESTRS. SINCE WE HAD 4000 FT SET IN MCP; ACFT AIMED FOR THAT ALT (HIGHEST ON SID). DURING ROLLOUT FROM TURN TO INTERCEPT THE RADIAL REQUIRED PER SID OUTBOUND; WE WERE ASKED WHAT ALT WE WERE GIVEN. THE CAPT REPLIED 4000 FT TO WHICH THE CTLR SAID TO LEVEL AT 3000 FT. AT THIS POINT; I ENGAGED THE AUTOPLT WE WERE AT ABOUT 2900 FT. I REALIZED THAT THE INFO HAD DROPPED OUT OF THE FMS; SO I QUICKLY TURNED OFF THE AUTOPLT AND LOWERED THE NOSE. WE GOT TO ABOUT TO 3200 FT AT THE HIGHEST. WE DIDN'T GET ANY TCAS WARNINGS OR TOLD OF ANY TFC CONFLICTS FROM DEP. SHORTLY AFTER WE LEVELED AT 3000 FT AND ON THE DEP WE WERE TOLD TO FLY A HDG AND CLB TO 4000 FT. I BELIEVE THE MAIN FACTOR WAS THE FMS DROPPING THE RESTRS ON ALTS AND ALSO MYSELF NOT CATCHING IT QUICK ENOUGH. ALSO; THE DEP DOES NOT HAVE A CLB-TO ALT BUT RESTRS ON POINTS WHICH LEADS YOU TO BELIEVE THAT YOU ARE CLRED TO CLB VIA THE DEP.