First of all, make a quick check of the DL25 (driving test report) given to you by your test examiner. At the bottom right, under "Licence rec'd", see if the "Yes" box is crossed. Did you sign the health declaration under that?
If so, the process works like this: The top copy of the report will have been posted first class to Newcastle or Cardiff (depending where in GB you took the test) then it will be in a queue waiting to be scanned (they get thousands every day) and the details forwarded electronically to the DVLA. Assuming the post arrived on Friday (you expect Royal Mail to be quick?) yours will be getting scanned any day now. DVLA should have you registered as a full licence holder round about the end of this week, but sh!t happens.
If you changed address recently and wrote your new address on the counterpart of your licence, the "COA" box will be crossed and even when the DVLA are made aware of your test pass, they will wait for your counterpart with new address to arrive seperately by post before issuing your licence. This is why your examiner told you to expect your licence to arrive in the post in around 20 working days.
If the "No" box is crossed, no action will be taken by the DSA or DVLA until you claim entitlement yourself by sending all your forms in the post.