B17 saddles are relatively long -- roughly 2cm longer than a typical modern racing saddle. I squirm back and forth on mine all the time, but I never feel like I'm sliding forward if I don't want to. You may want to try adjusting the nose up a tiny bit more.

Alternatively, you could try a different Brooks. I got a Swift for my next bike because it has a profile very similar to the old racing saddle I've done a gazillion miles in. Even a Brooks Pro is about 1cm shorter than a B17, IIRC.