Pilot flying reported a low altitude alert by ATC during a circling approach for landing at SFB. Pilot climbed to a safe altitude and continued approach.

Narrative

Arriving at SFB after a long cross-country flight under IFR; but in night VMC conditions (crystal clear and unrestricted visibility) to an airport and area that I was unfamiliar with I elected to execute the SFB RNAV 27R approach. I had two reasons -- one was to keep me 'safe' by following the IFR procedure; and the second was to assist in finding the airport. I declined a visual approach and requested vectors to the RNAV 27R. I was vectored on a left downwind during which I had visual contact with Runways 27R and 36. I was able to maintain visual contact with Runway 27R throughout the vectoring and approach.Approach control handed me off the SFB tower just outside the glideslope intercept and tower advised me that the winds were significant gusting out of 340; and asked if I wanted to circle for Runway 36. At this point; due to the clear weather; I was mentally unprepared for anything other than a successful completion of the approach to a landing on Runway 27R (as an aside; the ATIS indicating Runway 27R was in use). At this point; I was hyper-focused on the new winds report which exceeded my comfort level for a Runway 27R landing and accepted the tower's offer to circle. It took a few moments for them to get back to me to clear me for the circle; and at that point; I disengaged the autopilot from the approach and selected heading-hold mode to begin the downwind turn. Unrecognized by me at this point; the autopilot had already intercepted the glideslope and as a result left altitude-hold mode and entered pitch-hold mode; thereby continuing the descent. Lack of surface light contributed to me not immediately recognizing the descent.For sequencing; tower now asked me to extend my downwind away from the airport; which put me outside of the normal circling distance and also caused me to loose sight of the runway. I was unconcerned about this at the time; but in retrospect it put me outside of the IFR protected circling area. I believe the tower making this request of me was in error; and they should have given my arrival priority due to me being under IFR. I think both I and the tower were 'lax' about this due to the clear weather. In other words; once cleared to circle; the manner of my circle was entirely governed by the IFR rules; and my responsibility to follow them; both keeping the runway in sight as well as staying within the protected area. I briefly considered cancelling IFR to allow for more flexibility; but did not because I was unfamiliar with the nearby Class B airspace and didn't want avoidance to be my responsibility. I think an important distinction here was that I was 'cleared to circle southeast' as opposed to 'cleared visual approach'.During this downwind; I was hyper-focused on trying to see the runway; and over unlit terrain; both of which contributed to my delayed recognition that I was in an unsafe descent. I recognized it and started a climb just before tower gave me a low-altitude alert.In retrospect; I had two better options which would have broken the accident chain earlier. (1) I should have requested to execute the missed approach from the RNAV 27R which would have given me the time to mentally prepare for the Runway 36 arrival. (2) Alternatively; I should have stopped my descent and requested to overfly Runway 27R; entering a LEFT downwind for Runway 36. This would have done a few things -- it would have given me precious time to mentally prepare for the Runway 36 landing; it would have put me over lit terrain (the airport) which would have caused immediate recognition of the descent; and it would have put me into a 'circle left' position which would have made it easier to keep the runway in sight.