Birches Valley is usually locked when it gets dark.
A few park at The Horns pub just around the corner in Slitting Mill.
I've parked in the entry opposite Birches Valley before now.
You could park up near the other visitors centre at Marquet Drive but its a bit quiet (car safe?), & pick up the FtD at its mid point.
If your on your own I'd say park at The Horns.
We park at the White House as there is usually some lorries over-nighting there, hopefully meaning the cars might be safer. That way we can ride the FtD or some (better) trails over Sherbrook Valley way. You could tag along with us if you fancy it, we're not fast though & we ride for about 90mins max usually. (Just a mid-week tootle for us but if you fancy something different to FtD give us a shout).