Across:
   1,6. Quartet working with style for transmission (4 2 3 5)
  10. Backwater circuit (4)
  11,12. Baffled at elements of 'Base X' expansion, combining one on 99 with two on 28. (2 5 3 6)
  13. Our silly mixups in our heads (8)
  14. Mark they'll never meet we hear (5)
  16,19. Placed in awkward position, cheekily nibbled at heel, thigh (6 3 5 4)
  21. Use credit to steal (5)
  22. Cop? Sing out directions! (8)
  24. Bar serving tender (6)
  26. Job 16:51? (4 2 4)
  27. Good brief ... is taking little time (4)
  28,29. French hens perhaps shift on column (5 2 3 4)
Down:
   2. Element has region with its atoms 28ac. at a time (5)
   3. Wayward Helen rips top up (9)
   4. Lay snare about approaches (5)
   5. Chilli perhaps, eliminated time in care facility (7)
   7. Hangs in finals (5)
   8. Wish prone to compromise? (9)
   9. Use rigged exit poll mostly (7)
  15. Adventurous if he's with Haddock, perhaps (9)
  17. Utter words for directions (9)
  18. Some musicians engaged for gay feeling (7)
  20. Ban lies about favouring one's own kind (7)
  23. Shire eventually let go of old official (5)
  24. Fillets - the seconds removed (5)
  25. Problem child (5)