Twigesa
Most WP Advisors do not understand the limits the ESA claimants operate in.
As you have stated, as you are receiving ESA you are specifically not required to work or to seek work, however you can be required to perform Work Related Activity such as preparing a CV.
Also, WP Advisors have no authority to sanction a claimant, whatever benefit they are receiving, they can only make a request to the DWP for it to be done, the Decision whether to or not will be made by a DWP Decision Maker.
I would suggest that you contact your advisor and make them aware that you are receiving ESA, if you have no luck with this individual then escalate the issue to their supervisor.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems