Across:
1 Could be (= anagram indicator) aware (aware = EARWA-), mystery man (-X) (EARWAX) in 1 down is required to solve this problem perhaps (‘eardrops’ / EARWAX),
4 A (-A-) couple of Frenchmen (Messieurs = -MM-) in Press (press = SP-ERS) Box (= anagram indicator) (SPAMMERS) synonymous with The Mail no one wants (SPAMMERS),
9 Minister (RECTOR) responsible for 20 down (RECTOR responsible for ‘parish’),
10 Pin- (pin) -up (= reversal indicator) (pin = -NIP-) consumed by drink (drink/wine = WIN-E-) from grand (-G) (WINNIPEG) Canadian city (WINNIPEG),
12 Don Juan’s organ perhaps (ROVING EYE), I (I) heard (= homophone indicator) (‘I’ = ‘EYE) travelling around (ROVING), from the start (= position indication) (ROVING EYE),
13 Won’t get off on wrong foot? (‘wont’ get off on ‘wrong foot’ = rgfoo = FORGO) Give up! (FORGO),
14 Looks after flock (PARISH PRIEST) in community (PARISH) with ripest (ripest) bananas (= anagram indicator) (ripest = PRIEST) (PARISH PRIEST),
18 Those people at mass gathering (PARISHIONERS) found in 20 down (PARISHIONERS found in ‘parish’),
21 Some of those in Barcelona irritated (some of those in ‘BarcelONA IRritated’ = onair = ON-AIR) by broadcasting (ON-AIR),
22 One of those increasingly loud types (CRESCENDO) gets credit (CR-) for making (= anagram indicator) scene (scene = -ESCEN-) at party (-DO) (CRESCENDO),
24 Motivation (DRIVE-) for taking course of action (-WAY) (DRIVEWAY) – is that leading someone up the garden path? (DRIVEWAY),
25 Turns up (= reversal indicator) one (-I) pool (money/pot = -TOP-) is cold (-C-) for duck (duck = O-) (OCTOPI) and a number of molluscs (OCTOPI),
26 Revolutionary (= reversal indicator) in (in = NI-) welcoming address (-HI-) to Directory (-LIST) (NIHILIST) believes life is meaningless (NIHILIST),
27 Soup (BORSCH or borscht) in mug (rob = BOR-) taken up (= reversal indicator) by barman (Senior Counsel = -SC-) is hot (-H) (BORSCH).
Down:
1 They should improve the acoustics (EARDROPS) for adorable person (dear) losing the head (d) (‘dear’ without ‘d’ = EAR-) at a Bandon (a Bandon = abandon = -DROP-) school (-S) (EARDROPS),
2 Gets better (RECOVERS) for English (-E-) Club (-C-) investing in Dublin football team (Rovers = R-OVERS) (RECOVERS),
3 Concealed by Munro carrying (concealed by ‘muNRO CArrying’ = nroca) back (= reversal indicator) (nroca = ACORN) fruit from the forest (ACORN),
5 Highly value (PRIZE-) serviceman (-FIGHTER) (PRIZEFIGHTER) making a living in Ring (PRIZEFIGHTER),
6 Statement of intent (MANIFESTO) to clear (MANIFEST-) centre of bigotry (centre of ‘bigOtry’ = -O) (MANIFESTO),
7 Prime (prime) cut (= anagram indicator) (prime = EMPIR-) from Spain (-E) (EMPIRE) is big business (EMPIRE),
8 Join the club (SIGN ON) to get drunk (= anagram indicator) on gins (on gins = SIGN ON),
11 Sounds like (= homophone indicator) Jim has one of them (‘Jim’ = ‘gym’ has one of them = KEEP-FIT CLASS), as it’s designed for those who need to lighten up (KEEP-FIT CLASS),
15 Shaft (STAIRWELL) peer (stare) report (= homophone indicator) (‘stare’ = ‘stair’ = STAIR-) by Spring (spring = -WELL) (STAIRWELL),
16 Gatherings (REUNIONS) of neurons (neurons) going wild (= anagram indicator) (neurons = REUN-ONS) around centre of spine (centre of ‘spIne’ = -I-) (REUNIONS),
17 Shock (ASTONISH) as Martin’s travelling companion (ASTON- Martin car) is (-IS-) going to hospital (-H) (ASTONISH),
19 Noel Coward dismissed Carl (‘Noel Coward’ dismissed ‘Carl’ = noeowd = WOODEN) as an unemotional actor (WOODEN),
20 District (PARISH) of 14 across from the start (‘parish priest’ from the start = PARISH),
23 Captain Cook scrubs inkpot (‘Captain Cook’ scrubs/without ‘inkpot’ = caaco = CACAO) to use it for making chocolate (CACAO).