Cryptic crossword No 584

Across

1. Bang bang, like 2d, 23d, 6a, 8d, 12d and 14d (5,3)
2. Woman returns after struggle in city (6)
3. Writer’s critical friend is absurdly overtired (6)
4. Prosperous place for band of rats (8)
5. Consequences of time when Americans may have studied English (9)
6. Just can’t get enough to satisfy demand - not like the police in London? (5)
7. Welsh woman embraces Piper’s monkey (6)
8. Neater with bigger waves? (6)
9. The reflex is such a response to one tap on knee, poke around not required (6)
10. A noted lunatic made amends (6)
11. Small part in film turned up nothing (5)
12. Test alternative methods for cars here (9)
13. Most aggressive criminal certifies I disappeared (8)
14. Surge forwards about Jennifer (6)
15. Part of foot or hand in glove? (2,4)
16. Prescribes what person does to relax (4,4)

Down

1. Planet earth in 2022 possibly, crux of climatic roadmap - rowdy disorder building (8)
2. French composer made it a solo uplifting section (5)
3. Baggy trousers for band with sound system in Hampshire (5,5)
4. Relating to 80s music show, objection upheld over Yates essentially (6)
5. Love plus one, five and fifty construct instrument (4)
6. Sign of the times maybe, highly strung feeling follows close to me, causing delay (9)
7. Holiday is one of the first (3,5,3)
8. Temptation of far right country lacking holy figure (11)
9. Example of double negative for somebody giving donation by mistake (4,6)
10. Lose one’s way in between days on island (9)
11. Dead or alive perhaps, lesson about time (6)
12. See 2
13. Jump lead missing end acquires bit of power (4)
14. Broadcast introduction to songs of Wham (3)