Oyster Southern rail/LU advice please
 

I have a PAYG Oyster card. Today I have to get from Balham to Turnham Green
and was intending to take a Southern East CroydonMilton Keynes train that
goes direct from Balham. I'm intending to return by tube without using an
overground service.

Although PAYG Oyster cards are valid on Southern services via West Brompton,
I can't get through the barriers at Balham with my PAYG card so I assume
I'll have to buy a single ticket to cover me from Balham to WB and then use
my Oyster from WB to Turnham Green and for the rest of the day.

Unless, of course, you know differently...

Ian