Cessna P210 Single Pilot reported a CFIT event during final approach due to overshooting minimum altitude which was followed by an ATC low altitude alert. Pilot reported airport in sight and continued to a safe landing.

Narrative

While enroute to ZZZ; I was unable to begin my descent from my cruising altitude of 10;000 ft. MSL to the 2;000 initial approach altitude as early as requested and it led to a faster descent and speed than planned. As a result; the approach was much more hurried than normal; to comply with an expedited descent request and some communications difficulties between me and ZZZ Center and ZZZ Tower. All of this resulted in me arriving at the initial approach fix (ZZZZZ) on altitude faster than desired. I also wasn't sure if the ZZZ Tower expected me to fly the hold in lieu of procedure turn. I didn't think they expected that I would; which kind of made sense to me since my vector to ZZZZZ was very close to the approach course. When I looked at the approach chart I saw the notation that the hold in lieu of procedure turn wasn't required; but did not confirm this with the ZZZ Tower Just before reaching ZZZZZ I was still a little fast but felt that I was stabilized enough for the approach. Upon reaching ZZZZZ the Autopilot began the procedure turn so I disengaged the autopilot to continue direct to ZZZZZ1 and shortly thereafter the ZZZ Tower asked me to report at ZZZZZ1; which I acknowledged. I began my approach descent and broke out of the clouds at 1800 ft. and could see the airport. About half way to ZZZZZ1 the ZZZ Tower called and said they had a low altitude alarm and asked my altitude. I said I was VFR; had the field in sight and my altitude was 1300 ft.; which surprised me. They advised me to be very careful regarding possible obstacles. During flight planning I had reviewed the NOTAMs and chart to look for any obstacles on the approach and also took another look at my charts to confirm that there were none; so I continued my approach without returning to the required altitude. I also reported ZZZZZ1 when I passed the fix. HUMAN PERFORMANCE CONSIDERATIONS: After landing I gave a lot of thought to the approach. In summary; a number of things happened (i.e. late descent resulting in arrival at ZZZZZ too quickly and too fast; misunderstanding of some communications and relaxing my vigilance once I had broken out of the clouds and was VFR with the field in sight) during the approach; which resulted in me being overloaded. In the overloaded state I focused on the things I thought were most important: maintaining control of the plane; navigating to the airport and making a successful landing. I handled the Autopilot error in turning for a hold because I was hard wired to disengage it and continue direct to ZZZZZ1. I was disappointed by not maintaining the proper altitude to ZZZZZ1. When I broke out of the clouds and saw the airport I felt like I was now VFR; relaxed somewhat and mistakenly let my altitude descend below the 1;700 foot altitude before I reached ZZZZZ1. In retrospect; when the ZZZ Tower called me I should have also cancelled the IFR flight plan.In the last several years I've had ATC keep me at a pretty high altitude; necessitating a quicker; faster descent than I had planned; but this approach was more difficult than other's I have experienced. In the future; I think if this occurs I'll ask ATC for vectors to enable me to make the descent at more reasonable speeds and descent rates and allow more time for more communications with ATC and the Tower; if it is needed.