The Electoral Commission has issued guidance that clarifies who will receive a postal vote for the AV referendum in May, which you can download from their website here.
There are a number of variations for those people who have registered for a postal vote depending on which elections they have requested a postal vote for and whether there are elections in that area on 5th May. In summary though, the people who will receive a postal vote for the referendum is as follows:
people who have made a specific application to vote by post at the referendum, and this application has been granted
people who are on the standing postal voters list (definite/indefinite period) to vote at a UK Parliamentary election, or
This third bullet point is the one that has the most scope for confusion, as it means that people who are registered to have a postal vote in a council election only will only receive a postal vote for the referendum if they have local elections on the same day – this particularly affects people in London and those unitaries and districts that don’t have council elections this year, such as Cornwall, Shropshire, Northumberland, Wiltshire, Oxford, Gosport and Cheltenham (and a number of others).