After a system crash I ran svnadmin verify on some of the relevant repositories to check things were ok – this was done as root. Afterwards normal network access (via Apache) was broken with
Internal error: Berkeley DB error for filesystem
appearing in the logs. The fix was to chown -R www-data:www-data on the broken repositories. It looks like running svnadmin verify as root changes permissions on SVN repositories somewhere (at least Berkeley DB ones).
Lesson learned – check normal SVN access after doing this sort of thing!