General aviation pilot reported receiving a low altitude alert from ATC in VFR conditions on an IFR flight plan during initial climb. The pilot mis-read the SID chart instructions and failed to climb to the initial assigned altitude on the chart; then followed the ATC instruction to immediately climb and continued the SID.

Narrative

I filed for an IFR trip from BFI and was assigned a GPS SID southbound. The SID calls for an initial climb to 700 MSL on compass heading; 'then direct to' first GPS fix (about 10 nm from the airport); then on compass heading for radar vectors. The instructions conclude with 'maintain 2000 or as assigned by ATC.' The chart depicts 700 on the leg from the airport to the first fix but; in the past; after handoff the departure controller has always followed up radar contact with a climb instruction to above 2000. This time the controller was busy and looking at the chart I somehow thought it was indicating that I should remain at 700 until the first fix. My mistake resulted in ATC calling a low altitude alert and instructing an immediate climb; which I did without further incident. There wasn't any obstacle issue at 700 and the weather was VMC; but this unnecessarily distracted the controller and could have been much worse if circumstances had been different. I know better; but in the distraction of the moment I didn't do what was logically intended in the SID. I think an improvement in the SID instructions would be 'then direct to cross (GPS fix) at or below 2000' to emphasize the expected uninterrupted climb and top altitude. This is in fact the verbiage for the northbound SID.