Coalition government and benfits

Enigin mentions here the changes the new coalition government are putting in place and how they will affect those on tax credits and benefits.
The good thing about this new government, albeit a coalition one, is they have not wasted time getting down to the business of reducing costs the government cannot afford. Benefits are probably one of the highest outlays of government spending.
In the UK, the government assists those that are not so well off to be able to pay exorbitant rants in the capital and rents; those of which would put them at significant disadvantage financially given the lower rates of pay many working families receive.
Although the government would like to cut costs, there must be other areas of government spending that can be cut instead of benefits. What about increasing taxes to the rich? Surely it would be better to target those that have wealth rather than the have-nots. What about all those off shore bank accounts UK residents may have?
There are so many avenues the government can cut costs. Whatever little savings can be gotten by targeting assistance programs to the poor that cannot defend themselves against government cut backs, surely a better use of resources and man power would be to target the wealthy? This would also yield more money in terms of income. If the percentage of tax to earnings was raised for the better-off surely this would have a more favourable outcome all around, in terms of government income, and fairness to all those poor potential voters in the next election.