I'm sure you can guarantee fly tipping will increase which will in turn prove expensive if the council then have to clear it up. A word of warning though, if someone dumps rubbish on your land it's your responsibility to get rid of it, it has to be on public land for the council to get involved. There are many who couldn't be bothered to drive an extra mile or two to dispose of their rubbish before charges came in, it's bound to increase now. It also encourages households to have bonfires to dispose of certain types of rubbish too, such as fence panels whereas I would have though they were of some use if they were recycled them.
What I find particularly annoying though is that if evidence is found linking the rubbish disposed of to an address it is of little use as the person who originally owned the rubbish can claim they paid someone to take it away and it was not of their doing. The tippers have to be caught in the act which makes it very, very difficult to prosecute the guilty parties.
As far as reducing council costs by implementing charges I would have thought that a successful recycling programme could be self funding, there is a lot of metal and reusable household items that have an obvious value to start with. I'm told glass is ground down and added to tar and stones to make road coverings, paper is recycled too. Building rubble becomes hard core etc etc.
If the council really want to reduce costs they could begin by looking inwardly at under employed staff, overpaid management and big spending on things like council offices and the likes. Certainly household rates have gone up beyond the level of inflation for several years and yet we seem to get less and less in the way of a return.