Hi Chris
Providing your wife has at least 50 weeks of NI Contributions in both of the Tax Years 2017-2018 and 2018-2019 then she can make a claim for New Style ESA, this is a Contribution Based benefit so your household income, with the exception of any pension income you receive, is disregarded as are your assets and savings.
www.gov.uk/employment-support-allowance/how-to-claim She will also need to have a fit note (sometimes called ‘sick note’ or ‘doctor’s note’) but she can start making a claim before she have one.
New Style ESA is a Contribution Based benefit and is not means tested with the exception of pension income which can reduce the amount that you receive.
The Income Related benefit that goes with NS ESA is Universal Credit, UC will take into account household income.
Gary