Are double walled rims worth the money?
Extruded aluminum double wall rims are pretty much standard now (they are very much stronger than the cheap single wall rims).

Can you post a link on the bike you currently have ?

Cheap yet good quality wheel :

http://www.bike24.com/1.php?content=8;navigation=1;product=900;page=1;menu=1000,2,140,17;mid=0;pgc=0;orderby=2

Update :

OK - it is not a top quality bike, but still a good one that should last quite a bit with proper care (cleaning, lubing, changing chain when it's time, etc). Probably more than 10.000 km. Much much better than budget bikes that are totally destroyed after 1000-2000 km. 

So it makes sense to put a good quality 50€ wheel on it.

FYI, I just bought a wheel for 100€, it has a Shimano 3N80 dynamo (which is expensive), excellent quality spokes, and an very tough rim designed for loaded touring (forgot the name).

Basically in bike gear there are three broad "zones" :
- cheap crap
- reasonable price, reasonable quality
- expensive stuff whose purpose is mainly to shave off some weight or survive extreme conditions

Without dynamo, you can get a good quality wheel for 50€ if you shop around. Don't spend 100 quid, it's not necessary. But don't spend 20 quid, you'll get crap.