Overheating and battery light

Bought jimny recently, it is a 2006, done 55k and worked fine. I have noticed in the last few days a squeaking when in gear. 

This morning I drove it to work and at some point noticed the battery light come on, and then the temp gauge for right up to the top. I had to get to work so drove another 10 mins (max drive is 20 mins from home to work). A bit of steam coming out the lid (although cold morning and hard to tell) so opened the lid and the engine coolant was bubbling away like mad. 

Busted fan belt? Head gasket? All advice welcome as I am no car expert. Thanks!

The alternator and water pump are driven by the same belt which has clearly failed. That's £10 and 30 minutes to replace. But as you kept driving on an overheated engine you will invariably need to replace the head gasket in the near future, which is 10hrs work + £100 parts + £80 to get the head skimmed.

If you look under the bonnet, the belt that drives the water pump and alternator will be missing.

99% chance that the pulley on the crankshaft that should drive the belt is missing too (well the outside part that drives the belt)
1% chance that the alternator seized and the belt burned thin and snapped.

It needs a new belt, whatever is responsible for the belt loss- either a new crankshaft pulley or alternator and make offerings to the spirit of Suzuki Michio  that you haven't blown the head gasket and warped the head through overheating.

I once had a car where the water pump was driven by the cambelt (and had an electric fan) so I could drive it with no alternator belt to diagnose squeaking problems.  Wouldn't have risked it at night!