Hi Sonic,
Benefits & Work almost always recommend that if a claimant isn't happy with their current award that they submit an appeal to an Independent Tribunal, as before the DWP submit an appeal to the Tribunals Service to action, their award is automatically 'reconsidered' again by a more senior Decision Maker.
The benefits of an appeal is that the Tribunal see you, which Decision Makers never do. Reconsiderations tend to have around 10% success rate, whilst appeals are around 50%.
You can appeal online here:
Appeal against a benefit decision (leaflet GL24) Good luck.
Pat