GSM phone shops

Is it really impossible to get a pre-payed simcard without an address card -then you usually get a cheap phone with it for little money.
Anyway I know a second-hand phone shop at Jászai Mari tér - it is not where you asked but at the 4/6 tramline, pest side of Margit híd.
It is in the beginning of Pozsonyi út, on the right side when you come from the bridge, within 2 minutes. 
I haven't been to many of these shops and never bought a second hand phone, so I am just guessing that this one might be not very shady, at least I had no problem leaving an iphone there. Shiny West End shopping centre is one tram stop away, all major providers are there.
Of course, if you know what you want, you can buy stuff new on the internet and some shops have their outlet in cantral Budapest so you can pick the stuff up yourself. There is one such hardware shop near West End, but I cant recall the name.
argep.hu  is one of the  price-search-sites.