There is no specific reason why either benefit will be affected. You will need to notify the DWP in regard to your ESA claim as this will come under Permitted Work rules, there is a guide in the ESA section. You are not required to notify PIP.
All that said, if your starting work is the result of an improvement in your conditions, likely to result in a change to how you previously qualified for your awards then you are required to notify both ESA and PIP about this.
The likely result will be a full reassessment of both claims, this could leave them as they are but it can also lead to a reduction or even the removal of one or both awards, so think carefully before starting the work.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems
