Hi James,
That depends entirely on whether your ESA is contributory or income related. If it is contributory then your partner's income/assets will not affect it, if your ESA is income-related, in part or in whole, your partner's income/assets must be declared and could reduce the amount of ESA you receive. I cannot tell you an exact figure as this also depends on whether you are entitled to any ESA 'premiums'.
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
