No special access issues
The old parking lot (at Koviks hagar) is closed long ago with a road barrier. Some cars park along the road just outside the barrier. No repports on tickets but this might not be allowed. It is allowed to park IN THE VILLA AREA along Hermelinvägen but not outside the villa area. Make sure not to block entrances to the houses or park less than ten meters to any intersection. Then walk back and turn right in to the woods at the big bearsign. Follow the path. After about 100 meters the path turns out towards a field. Follow the path along the field edge. After about 250 meters the path divides (at a nature sign) follow the path around the forest grove to the left or right and soon you are inside Skevik's cave.
The walk takes about seven minutes.
Public transportation:
Take the bus to Koviks hagar. Takes 35 to 55 minutes from Slussen.
https://sl.se/en/