How long can I drive my car for after battery light came on?

I have a 2001 ford ka and earlier today the battery light on the dashboard came on, I googled what it is and think it's the alternator. I'm getting it serviced next Wednesday but need to make a 40 minute journey tomorrow but not sure whether to risk it or not?

You will not make it if the battery is not being charged. The service wil not cover your problem either, you need to book it in for diagnostics.

I'm presuming you have checked the obvious like the axillary belt has not snapped?

Unless you have a battery charger and can fully charge the battery overnight, it is unlikely the car will start tomorrow. If the belt came off, you won't get far since the water pump also runs off that belt.

You Google and you suspect the alternator is out? Sure. Go with that. But make sure the serpentine belt is still in the car. You can drive to the nearest auto service center to have the car's alternator replaced. To pretend all is OK as long as the batter has power is not smart and not recommended. The battery is not designed to power the car for extended periods of time. It shall overheat and get ruined. Then you shall need a new battery plus the alternator.

If the battery is fully charged and you are driving with no lights and no A/C and no radio, you can go quite a ways.
If it is 40 minute round trip You might chance it. If it is 40 minutes one way. That could be a long long walk. Can you take along a 2nd fully charged battery?

I would make other arrangements, when your battery is completely dead, you will be walking home. Assuming your alternator has failed you have about 30 mins of drive time, 20 with your lights on.

I would test the alternator and make sure it is actually your problem. I would also test the battery and here is how to do both easily.

How to test alternator

How to test battery

Do this and you won't need to pay someone to test it. Plus, if your alternator is bad, the car could die at any time when your are driving so it isn't worth the risk!

Get it checked quick

You have a Ka, a small car with a small battery. It could be the alternator belt slipping, or could indeed be the alternator. I certainly would not risk a 40 mile drive, come to a halt half way and unless you have AA/RAC/Green Flag breakdown insurance you will have a hefty tow truck bill to pay.

Short answer, no chance. A small battery will give out after 10-15 minutes on no charge, and that's assuming it was fully charged to begin with, which yours probably isn't.

I had a ford Windstar that I drove for a couple days with the battery light on, the alternator had quit working. But this was a regular size battery. Your battery is smaller and I'm not sure how much power your car would need to keep the computer running.
I would not chance it, if you have a battery charger plug it in overnight and then go. Take it to one of the national auto parts stores and they might be able to check your charging system for free.