On the edge of the car park I backed into the next available spot: Grammar Check

This sentence is grammatically correct and does not require a comma. "On the edge of the car park I backed into the next available spot." is a simple sentence with a subject (I) and a verb (backed). The phrase "on the edge of the car park" acts as an adverbial phrase modifying the verb "backed." It is not necessary to separate it from the main clause with a comma.