Pretty tricky one! Hadn't heard of 6A or 13A, and plenty of reasonably difficult clues elsewhere. Figuring out the parse of 16D was a struggle: "top" to remove the first letter combined with a synonym is a hard mechanic.

Across

1

Vocalise about wine that's unspeakable (8)
SHOCKING — SING (vocalise) around HOCK (wine)

6

Gang busters in the middle of a drink (6)
POSSET — POSSE (gang) T (middle letters of busters)

9

Outcry on surprise introduction of British English to Americans (6)
BLIMEY — B (first letter of British) LIMEY (English to Americans)

10

Switched caboose around to the front line (8)
VANGUARD — cryptic def.

11

Bazaar fortune telling (4)
FETE — homophone (telling) of FATE (fortune)

12

Printed works turn into misprinted air letter (10)
LITERATURE — U (turn) inside anagram (misprinted) of AIR LETTER

13

Smoke after function in work-free office (8)
SINECURE — SINE (function) CURE (smoke)

15

Turn one's back on the deep red (6)
MAROON — double def.

17

Small flat earring with single ring (6)
STUDIO — STUD (earring) I (single) O (ring)

19

A minister accepted Conservative leader's right (8)
ACCURATE — A C (first letter of conservative) CURATE (minister)

21

Cut back on observing rain or shine (10)
REGARDLESS — REGARD (observing) LESS (cut back)

24

Impressive stripped and flexed biceps ... (4)
EPIC — anagram (flexed) of bICEPs (without outside letters)

25

... of undressed models wear thin (2,3,3)
IN THE RAW — anagram (models) of WEAR THIN

26

Get down when lit up (6)
ALIGHT — double def.

27

Fine spray to be heard but not seen (6)
MISSED — homophone of MIST (fine spray)

28

Most recent gents outfit behind second person's pronoun (8)
YOUNGEST — YOU (second person's pronoun) anagram (outfit) of GENTS

Down

2

Latin in the lines put off student of Greek (9)
HELLENIST — anagram (put off) of THE LINES L (latin)

3

Strive to show up outside favourite (7)
COMPETE — COME (show up) around PET (favourite)

4

Happy story duly ends in misfortune (5)
IDYLL — DY (outside letters of duly) in ILL (misfortune)

5

Blow the whistle to end sporting career (4,3,4,4)
GIVE THE GAME AWAY — cryptic def.

6

Taking a broad view of a man or monster in photo (9)
PANORAMIC — anagram (monster) of A MAN OR inside PIC (photo)

7

Leisurely walk set a run off (7)
SAUNTER — anagram (off) of SET A RUN

8

Slip up in charter or register (5)
ERROR — hidden in chartER OR Register

14

All thrown together and not wanted on the menu? (9)
UNORDERED — cryptic def.

16

Top price to put on wealth by those in a dream world (9)
OSTRICHES — cOST (price, without first letter) RICHES (wealth)

18

King, say, set up British warship with masses of drugs (7)
DRACHMS — reversal (set up) of CARD (king, say), HMS (British warship)

20

Swimming after electric swimmer broke circuit (7)
REELING — EEL (electric swimmer) in RING (circuit)

22

Reunion put off or abandoned through lack of interest (5)
ENNUI — anagram (abandoned) of rEUNIoN without or

23

Complete confusion by guiding us around cooler set-up (5)
SNAFU — reversal (set-up) of US around FAN (cooler)