Can the defendant in civil litigation ask the claimant for documents while waiting for the allocation questionnaire to be filed or can a defendant ask for documentation at any time after the claim was issued or does he have to wait until after the filing of the allocation questionnaire by the two parties, bearing in mind the defendant and claimant have no solicitors at this stage

Really this should have been done before the defence was filed, under CPR 18.
After all how can a fully particularised defence be entered if the complete facts of the case are unknown.

What type of case are you involved in here ?

As soon as the case is filed, discovery motions can be filed.

Scott, this guy is in the UK, so it's slightly different ;)

For a change I know the procedure :D:D

I figured UK as soon as he said solicitors. But the idea of Discovery should be pretty similar.

Yep, tis indeed.
We are cover by CPR, The Civil Procedure Rules.
These cover how Civil cases are to be run.

As a Litigant in Person there are certain leeways that are given especially in respect to information and filing of documents.
The Allocation Questionnaire (AQ) is used to help the Judge determine the best "Track" for a case.
There are three in the UK.
Small Claims - Sub £5k
Fast track - £5k - £15K
Multi Track - £15K+

Most of the work I do is in the first two tracks, but against well funded claimants, i.e. Banks ;)