https://www.gov.uk/overseas-passports
Be aware that first British passport applications for British citizens by descent children born in the Subcontinent can take six months to a year. So factor that in in case your wife is on a visa.
Also be aware that while the child itself will be a British citizen by descent, their children (your grand children) born outside the UK will not automatically be British citizens. British citizenship is restricted to one generation born outside the UK.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.