The Liberal Democrat Chief Secretary to the Treasury said that numbers "vary". But a Labour MP described the answer as "astonishing".
The row between the LibDems and the Tories over Trident flared up again when LibDem leader Nick Clegg railed against spending billions on a system designed to flatten Moscow.
But the Tories are committed to a like-for-like replacement.
The two UK Government parties have agreed to postpone the final decision until 2016 but Mr Alexander is in charge of a review into alternatives.
Dunfermline and West Fife MP Thomas Docherty asked him how many civil servants and military personnel had been assigned to work on the review. Mr Alexander said it was being led by Cabinet Office officials and would consult experts in other departments "on an as-required basis". He added: "The number of experts in each department varies with the different stages of work and the type of expertise required."
But Mr Docherty said: "The fact that they either can't or won't say how many people are working on it is astonishing."