There is a parking place in Balham not far from the traveloge. You should be able to google parking in Balham or contact the traveloge . Hope that helps.
Parking is a pain. You can park on the road next to the hotel from 5pm to 9am.l, if you can find a spot.
You can park your car overnight on the road , but be very carful to read the signs.
Get an answer from Travelodge London Balham staff and past guests.