Contact and Activity exports throw SQL error

Encountered on 3.4.3 and replicated on demo r34843. Both contact and activity export throw a SQL error.

Steps to replicate - Contacts.

(1) Find Contacts, any or no search criteria. (Same from Advanced Search as Contacts.)
(2) Select Export task.
(3) Either primary fields or select fields.

Result: CSV is exported with some contacts, but underneath these in the CSV is a page of HTML with an error like:

DB Error: no such table
Database Error Code: Table 'civicrm_demo_drupal.civicrm_export_temp_8620bbfe17f45217db2c13f913c2a484' doesn't exist

Steps to replicate - Activities.

(1) Find Activities, any or no search criteria. (Same from Advanced Search as Activities.)
(2) Select Export task.
(3) Either primary fields or select fields.

Result: CSV is exported with some activities, but underneath these in the CSV is a page of HTML with an error as above.