JediCP
The DWP can average earnings and hours but only by prior agreement, however, you do need to be aware that the 16 hours and £115.50 after tax and national insurance deductions, are absolute limits if you are considered to have exceeded them then your ESA claim will be closed.
It sounds like you need to speak to your potential employer first to see whether they can accommodate you in the first place and then you need to contact the DWP.
There's a guide to PW in the ESA section.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems