A class mercedes 160 BAS ESP light came on after a mile drive

check and test abs system and or hubs for failure Finally Fix Mercedes class ESP ABS BAS FAULT LIGHT Malfunction

yes

BAS = BRAKE ASSIST SYSTEM
ESP = Electronic Stability Program

All you have to do after replacing the battery and the bas/esp light comes on is drive the vehicle. While your driving around is will allow the steering angle sensor to relearn. That's only if it says "bas/esp see owners manual" displayed on the cluster.

check brake light switch and replace it, it's most common fault. is this information helped you. please vote me and leave a comment.

it's the brake switch, located behind the brake bedale , just replace it and every thing will come to normal.

replace the brake switch

What it sounds like is the antibrake module took a dump. Most likely needs to be rebuilt. Modulemaster.com can do this for alot less that a dealer replacement. You can still drive the car but you do not have the antiskid capabilities the system has to offer. Good thing its summer. Get it fixed ASAP

Brake Assist System, Electronic Stability Programme. It will need to go on a computer, the most obvious thing is the brake light switch, fault will need to be erased after fixed.

Change the brake light switch first, its on the brake pedal, £9 from mercedes.
jib
www.mercanic.co.uk