I found a sett a few years ago, scoped it out a few times, never saw a badger. I left a trail camera out, which was a big risk as dog walkers frequented the area. It never triggered but there were definately badgers present.
I hear they love raisins, so might be worth scattering a few and wait to see what happens.
The biggest problem is though that they forage at night and this time of year, they still have plenty of dark hours to do their scavenging.
My approach would be to wait until the summer months, when there are only a few hours of darkness, end of May to the begining of July, when the dark hours are much shorter, in fine weather, it hardly gets really dark at all during the middle of that period. My approach would be to camp nearby as the badgers will almost be forced to forage during lighter hours, even in daylight, it can easily light enough by 4am.
I think this is maybe your best chance without flash, as at the moment, it will be too dark when they forage anyway. You may be lucky and have a group that forage during the twilight hours at the moment but I'm guessing not.
As is usually the case with wildlife, patience and fieldcraft will usually reap its rewards.
I really must take a look at my locals this year.