A B737 CAPT RPTED THAT A LEADING EDGE FLAP PROB CAUSED HIM TO EXECUTE THE MISSED APCH AT DCA AND THEN TO DECLARE AN EMER AND RETURN FOR LNDG.

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WE WERE TURNING BASE TO FINAL FOR THE VISUAL TO RWY 1 AT DCA AND EXTENDING FLAPS FOR LNDG. WHILE EXTENDING FLAPS 10 DEGS; WE GOT A LEADING EDGE FLAP IN-TRANSIT LIGHT ON THE FORWARD INST PANEL WHILE WE WERE ON FINAL APCH. WE THEN BROKE OFF THE APCH AND GOT RADAR VECTORS WHILE WE WERE DOING THE IRREGULAR PROC. WE ACCOMPLISHED THE 'LEADING EDGE FLAP TRANSIT LIGHT (FORWARD PANEL) ON' IRREGULAR CHKLIST. WE THEN TRIED TO CONTACT DISPATCH VIA VOICE AND WERE NOT SUCCESSFUL. WE COULD HEAR THEM; HOWEVER; THEY COULDN'T HEAR US. WE WERE AT 3000 FT MSL AND I SUSPECT THAT THIS WAS PART OF THE PROB; IN BEING AT A LOW ALT. I THEN CONSULTED THE IRREGULAR LNDG DISTRIBUTION CHART THAT TOLD US WE NEEDED 3500 FT FOR LNDG; WHICH WAS OK FOR OUR RWY. WE WERE FINALLY ABLE TO GET AN ACARS MESSAGE OFF TO DISPATCH AND TOLD THEM OUR PROB AND THAT WE FELT IT WAS OK TO LAND AT DCA. THEY AGREED AND; IN TURN; DECLARED AN EMER ON OUR BEHALF. ADDITIONALLY; WE DECLARED AN EMER OURSELVES. I TOLD THE FLT ATTENDANTS TO PREPARE A CABIN ADVISORY. WE THEN TOLD ATC WE WERE READY TO LAND AND LANDED UNEVENTFULLY. ON ROLLOUT; I HAD THE FO TELL THE FLT ATTENDANTS TO REMAIN SEATED. THIS ACTION WAS PROBABLY NOT NECESSARY; SEEING THAT I HAD THE CABIN PREPARE FOR AN ADVISORY. WE THEN PULLED OFF INTO THE RWY 19 RUN-UP PAD AND REQUESTED THE EMER EQUIP TO INSPECT THE BRAKES; WHICH TURNED OUT TO BE FINE. WE THEN PROCEEDED TO THE GATE AND WERE MET BY MAINT. I THEN CALLED DISPATCH AND CONFERRED WITH THEM.