"As long as we don't bail out the banks again or finance any more unjustified wars."
Neither are really responsible for our overspend and are both convenient excuses held by people trying to divert attention from the real cause, which is simply the idea that we can keep spending more than we earn.
In terms of "unjustified wars" I presume you mean Iraq (which was very dubious) and Afghanistan (which was a commitment under the NATO treaty). The actual extra cost of those wars on top of the NHS budget was £20 billion over ten years, so £2 billion a year for both conflicts. Here's a very left wing paper which quotes that figure, other places do to, so it's presumably accepted: /view/full/91782
To put that £2 billion a year into context over the last financial year the Government overspent by £140 billion. In comparison we spend about £95 billion a year on the NHS and £135 billion on benefits. £2 billion a year would barely make a difference, it certainly wouldn't fix our problems. That's not to say that it wouldn't help, but that it's not the answer.
And as to the bankers I don't believe that any of that £140 billion overspend was given to banks. Most of what we've done with the banks is to guarantee bad debts rather than pay out hard cash. So even giving money to the banks is not responsible for out £140 billion overspend either.
Neither our military conflicts or our bankers are responsible for the hole that we're in. They're both excuses offered up primarily by the left wing to cover up the mess that refusing to tackle this problem has lead to. The excuse given by the right wing is usually to blame Labour when while they were in power they refused to balance the books and ignored the problem too.
"Complete reform of the tax system is needed more urgently than a botched reform of the NHS."
Yes. We need to bring the books into balance and live within our means rather than pay for our lifestyles with credit and lumber our children with the pain later. Every day that we run around kidding ourselves that wars, bankers or socialism are the cause is just another day spent with our heads buried in the sand.