ACROSS
 1. <bureaucratic> KAFKAESQUE = F_K inside SEAQUAKE*
 6. ←BLUB← = BULB <onion?>
10. <vexed> HET UP = HE + ←PUT←
11. A + CROP (ET AL) = ACROPETAL <growing upwards>
12. ←WAR← "HYDE" = RAWHIDE <Eastwood show>
14. <leaves> SPINACH = SPIN + A CH
15. <big> BROBDINGNAGIAN = BRO B_D IN ←GANG← I_ A_ N_
18. <sports venue> WEMBLEY STADIUM = W EMBLE[-m] + (A TIDY SUM)*
22. CHAP AT_ I = CHAPATI <flatbread>
23. <I lead> PIONEER = ONE inside PIER
24. OVERSEER outside T = OVERSTEER <faulty turning>
25. <Nobel-winning physicist> HIGGS = HS outside I (G G)
27. <girl> LASS = LA'S S_
28. ←(.m)AN VERA'S EST(r.)← = TSESAREVNA <heiress>

DOWN
 1. ←I BAR L_H + OK← = KOHLRABI <greens>
 2. <sexy> FIT = F + IT
 3. <used> APPLIED = APP L_ IED
 4. <cliché> STALE = S_ TALE
 5. PRISING inside US = UPRISINGS <rebellions>
 7. <blue> ULTRAMARINE = U (MATERIAL RN)*
 8. <awkward> BOLSHY = ←LOB← + SHY
 9. SP R IN G_ = SPRING <source>
13. <vendors> WHOLESALERS = "HOLE SAILORS"
16. ←SEEN← outside DINES = NEEDINESS <poverty>
17. (A BAR + MISO)* = AMBROSIA <heavenly food>
19. <stew> BRAISE = "BRAYS"
20. A (NOT HER) = ANOTHER <again>
21. <navigate webpage> SCROLL = S C ROLL
23. PARISH - H_ = PARIS <city>
26. <boss> GUV = G UV