The resignation comes a day before the winner of the Tory leadership race is announced.
The dogs are based at the Defence Animal Centre in Melton Mowbray, Leicestershire, part of Sir Alan's constituency.
More than 100 "very serious prisoners" have escaped from jail on the British Virgin Islands.
International development minister Alan Duncan has said the situation in the Philippines is a "disaster of cataclysmic proportions" after it was hit by a super typhoon.
He told ITV News: "This is absolutely as bad as it gets. We are looking at a disaster of cataclysmic proportions, so the whole world community now has to say 'it's all hands on deck'.
"In the UK we've already chartered five flights within 48 hours and we're going to get basic life-saving kit there as quickly as we possibly can".
International development minister Alan Duncan has been visiting injured survivors of the Rana Plaza factory collapse in Bangladesh.
Read Laura Kuenssberg's blog: Government expects UK retailers to increase standards in Bangladesh
The government has told ITV News that they will expect UK retailers to make more of an effort to drive up standards in Bangladesh.