In six answers the wordplay ignores an item. These items (two of them identical) are not listed as specific 27 of 22 in Chambers, unlike the other unclued entries.
 

Across

 
1    Extra thin pins cleaned up with this? (5)
6    One that’ll teach you a measure of warmth (8)
12    Hopes dashed with 31 restaurants (10, hyphened)
13    Horse runs into different one (9)
14    Allan Wells, perhaps, absent from racetrack? (4)
15    Censor adjusted EastEnders, essentially as seen on TV (8, hyphened)
16    Stick holds sack, calculating its volume? (6)
17    Problem when 22 for a group’s composition (5)
21    One spreading malicious rumours about banker’s return (11)
24    Sleeper props up railway in the end (3)
26    Strike — that gets you to first base? (3)
28    Having a stellar cast that omits no-one ultimately? (7, hyphened)
33    Fly around left of the sun (5)
34    Duck with half-inch of bone (6)
35    Old nag, who wears the trousers in a saying? (8, two words)
37    Performing group dispensing with hard and tough material (4)
38    MP leans on strange glowing objects (9, two words)
39    Play down the condition of slavery? (10)
40    Most dark ties must be knotted (8)
 

Down

 
1    To do this might make fin soapy? (8)
2    Protein shakes with son that may be prematurely conceived? (10)
3    Eldest sons said to put these on? (4)
4    Secrecy almost ruined scouting parties (6)
5    Sea creature almost eats bird up, tiny sea creature (11, two words)
8    Get fit, expending energy fast (5, hyphened)
10    Food when American turns to go — not fast food! (9)
11    Child (perhaps following man) leaves city compound (5)
18    Some work common to clergymen and covergirls (3)
19    Hard substance wrapped round a bone (10)
20    Security almost accepted by charity, a foul matter (9)
23    Was a gardener about finished getting tidied up? (8)
25    They provide support for member, member involved in stoppages (8)
28    ‘Eat’, with a tense shifted (3)
30    One wandering around unsettled? (6)
31    Cheat this American (5)
32    Rambling confession upset native (5)
36    Macmillan regularly cut down tree (4)
 
A first prize of £30 for the first correct solution opened on 4 May. There are two runners-up prizes of £20. (UK solvers can choose to receive the latest edition of the Chambers Dictionary instead of cash— ring the word ‘Dictionary’.) Entries to: Crossword 2207, The Spectator, 22 Old Queen Street, London SW1H 9HP. Please allow six weeks for prize delivery.