Doc is the compiler of this Spectator crossword.
The preamble to the puzzle reads as follows:
The unclued lights can be arranged to grow from 3 to 11 letters in length, each being an anagram of its predecessor and an extra letter.
Apart from a couple of obscure references (at least to me), including nattier blue and Polari, this was mainly a straightforward and enjoyable solve. It was just difficult enough to be satisfying to solve. The string of words from 3 to 11 letters (highlighted in the grid below, starting with EAT and ending with INCINERATES) wasn’t difficult to work out although I had to check that NECTARIES was a word.
Thanks, Doc.

| ACROSS | ||
| 1 | INCINERATES |
(11)
|
| 7 | BAT |
Equipment for Bell, Athey and Trescothick initially (3)
|
| B(ell) A(they) T(rescothick) [initially]Ian Bell, Bill Athey and Marcus Trescothick were all English batsmen. | ||
| 11 | RECANT |
(6)
|
| 13 | MENACES |
Male folk star’s alarming words (7)
|
| MEN (“male folk”) + ACES (“stars”) | ||
| 15 | BRIAR |
Pipe valley running through Britain (5)
|
| RIA (“valley”) running through Br. (Britain) | ||
| 16 | STAID |
Reportedly remained stolid (5)
|
| Homophone/pun/aural wordplay [reportedly] of STAYED (“remained”) | ||
| 17 | MESIAL |
Middle of emails edited (6)
|
| *(emails) [anag:edited] | ||
| 18 | BIDET |
Nameless President has time on the loo (5)
|
| (Joe) BIDE(N) lacking an N [nameless] has T (time) | ||
| 20 | CRANIA |
Brainboxes managed to infiltrate spy agency (6)
|
| RAN (“managed”) to infiltrate CIA (Central Intelligence Agency, so “spy agency”) | ||
| 21 | PETER |
Thorpe, terrified somewhat of safe-cracker (5)
|
| PETER (“safe”) cracking into “thorPE TERrified” [somewhat] | ||
| 22 | REELING |
Doddery, maybe, when dancing in Aviemore? (7)
|
| Double definition | ||
| 27 | CERTAIN |
(7)
|
| 29 | ARRAS |
Hanging back in disarray (5)
|
| Hidden [back in] “diSARRAy” | ||
| 30 | ELAPSE |
English earl touring alps negotiated pass (6)
|
| E (English) + E (earl) touring *(alps) [anag:negotiated] | ||
| 32 | AORTA |
Blood carrier, a kind heading off on ambulance initially (5)
|
| A + (s)ORT (“kind” with its heading off) on A(mbulance) [initially] | ||
| 34 | POLARI |
The North Star gets cut in form of cant or slang (6)
|
| POLARI(s) (“The North Star”, gets cut)Polari is a form of slang used in some British subculutures and professions. | ||
| 36 | ULCER |
Blemish beautiful cereals boxes (5)
|
| Hidden in [boxes] “beautifUL CEReals” | ||
| 37 | CATER |
(5)
|
| 38 | RWANDAN |
African who gets the stick, having rushed around (7)
|
| WAND (“stick”) having RAN (“rushed”) around | ||
| 39 | REGION |
Area occupied by some flustered foreigners (6)
|
| REGION is an anagram [flustered] of several contiguous letters of (f)OREIGN(ers) | ||
| 40 | EAT |
(3)
|
| 41 | SUSAN GEORGE |
She played Amy for Sam in 1971 with Sarandon and Clooney (5,6)
|
| SUSAN (Sarandon) and GEORGE (Clooney)The actress Susan George played a character called Amy in the 1970 thriller Straw Dogs, directed by Sam Peckinpah. | ||
| DOWN | ||
| 1 | IN MEMORIAM |
Collapsed mine with folly marks final tribute (2,8)
|
| *(mine) [anag:collapsed] with MORIA (“folly”) + M (marks) | ||
| 2 | CANISTER |
(8)
|
| 3 | NECTARIES |
(9)
|
| 4 | RESTING PLACE |
Tracing sleep maybe, and where to find it? (7,5)
|
| *(tracing sleep) [anag:maybe] | ||
| 5 | TALIBAN |
Fundamentalist army replace subhuman’s head with time (7)
|
| Replace the head of CALIBAN (a subhuman in character in Shakespeare’s The Tempest) with T (time) to get T(ALIBAN) | ||
| 6 | STRIDENT |
Second passenger aircraft making a lot of noise (8)
|
| S (second) + TRIDENT (“passenger airport”) | ||
| 7 | BRIBE |
Born to make fun of drug incentive (5)
|
| B (born) + RIB (“to make fun of”) + E (ecstasy, so “drug”) | ||
| 8 | TARE |
(4)
|
| 9 | LEXEME |
Latin law primarily explaining Middle Eastern linguistic unit (6)
|
| LEX (“Latin” for “law”) + [primarily] E(xplaining) M(Iddle) E(astern) | ||
| 10 | BASIC |
Elementary book academy faithfully reproduced (5)
|
| B (book) + A (academy) + SIC (“faithfully reproduced”) | ||
| 12 | NATTER |
Chinwag with Blue. I left (6)
|
| I left NATT(i)ER (a shade of “blue”) | ||
| 14 | DAVID CAMERON |
Random advice doled out for PM (5,7)
|
| *(random advice) [anag:doled out] | ||
| 19 | TRANSIENCE |
(10)
|
| 21 | PARSONAGE |
Priest’s crime taking time in clerical residence (9)
|
| P (priest) + ARSON (“crime”) taking AGE (“time”) | ||
| 23 | LEARNERS |
Fifty folk with a wage are beginners (8)
|
| L (50, in Roman numerals) + EARNERS (“folk with a wage”) | ||
| 24 | MARAUDER |
Pirate state with a Durer composition (8)
|
| MA (Massachuetts, so “state”) with *(a durer) [anag:composition] | ||
| 25 | FRACAS |
Amateur in neckwear raised uproar (6)
|
| A (amateur) in <=SCARF (“neckwear”, raised) | ||
| 26 | SEA LEGS |
The Navy’s firmest supporters (3,4)
|
| Cryptic definition | ||
| 28 | INROAD |
Attack the entranceway? (6)
|
| IN (“entrance”) + ROAD (“way”) | ||
| 31 | ELAND |
Animal making dash, getting trapped ultimately (5)
|
| ELAN (“dash”) getting (trappe)D [ultimately] | ||
| 33 | OCTET |
Musicians content to leave Egypt after 31 days (5)
|
| [content to leave] O(cte)T after Oct. (October, so “31 days”) | ||
| 35 | OCHE |
Pinochet drops pint here? (4)
|
| (pin)OCHE(t) drops PINTThe oche is the line from which a darts player throws their darts. | ||