VW
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A Paper based Appeal, one that you do not attend, can be held at any time once the one month you are allowed to make your submission has passed. They tend to be heard sooner rather than later.
You can make a new claim for PIP at any time, there is no waiting time between claims, however you cannot back date prior to the date that the claim is made.
You need to be aware that as a new claim will result in a new Decision being made, so it will limit any result that a Tribunal might make, so if the Tribunal finds in your favour and there is no award from the new claim, then the nil award will supersede the Tribunal one from the date it is made, you therefore might want to wait and see the Tribunal result before making a new claim.
Gordon