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It would only be an issue if you were receiving the Severe Disability Premium but this would appear not to be the case unless the wife also has a qualifying award of DLA or PIP.
The CA will be deducted from your ESA but you will receive a Carers Premium of about £35 per week, leaving you better off.
I would run the situation through one of the online benefit calculators before making any decision to claim the CA.
www.gov.uk/benefits-calculators Gordon
