The reason they pushed for it? Basically, private banks were printing too many banknotes and causing bouts of inflation. This was in a time when currencies were still backed by gold.
Here is the speech by Robert Peel that convinced Parliament (as well as myself) that this was a good course of action to follow: http://www.historyhome.co.uk/polspeech/bank.htm
If you made a papery currency, what is it backed by? A big pile of gold? Do you have a lot of men with guns defending that big pile of gold?
What is backing a fiat currency like the $US? Trust that the country will continue to exist? The might of the armed forces? It is a number of things, but the conditions are very difficult to reproduce without a lot of cold, hard steel moving around at high speeds through land, sea, and air.