The Passport Office chief executive Paul Pugh said the agency was facing a challenging situation the like of which has not been seen in recent years, after apologising for the delays.
He said the Passport Office is dealing with 480,000 applications. Around 90% are being processed within targeted time.
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Owners must also prove they have something to pick up dog mess with under new rules imposed by one council.
The former prime minister made the comments as he prepares to return to politics saying he wants to be "part of the debate" on Brexit.
The new measures would mirror childcare vouchers and see workers sacrifice some of their salary to benefit.