I think his wife would not be eligible in this ESTA..as it states they have to be a citizen or a national of one of the Visa Waiver Program countries, and Philippines is not included. UK is included, but unless she's already a British citizen, she can't avail this. She has to apply for visa in the US Embassy.
Oh yes, ESTA is not a visa ....the wife can apply for B-2 visa with the US Embassy in London but ''both of them still need a valid ESTA to enter the US or transit to any US Channel''.