Hi Paula
At present, when you ask for a reconsideration and the DWP send you a letter telling you that they refuse to change their decision, you have one month from the date of this letter to appeal.
The only thing that's likely to change when the Welfare Reform Bill gets passed is that you will no longer be able to appeal straight away. You will have to apply for a reconsideration first, but you will have an additional month to appeal if the reconsideration does not change the decision.
Hope this helps
Derek