Gap year programmes at low cost? Watch
The European Voluntary Service offers projects of up to a year, funded through the EU, so actually there is no cost to you, you even get a bit of pocket money. I am 8 months into an EVS project so feel free to ask me about how it works if you want.
The other way of going abroad to volunteer without paying a fortune would be through Workaway. You pay your travel costs but do get full board in exchange for your work :-)