Answers in BOLD CAPS. Definitions in italics underlined. Taking my cue from Jackkt I have included more explanation than long-time solvers will want in order to be of use to more recent enthusiasts.
1. Abolish hotel by river where people go to eat (9)
CHOPHOUSE CHOP=abolish (slightly odd def.). H=hotel in phonetic alphabet. OUSE=river.
6. Mineral from drinking goblet, not one put on back of lorry (10)
CHALCEDONY CHAL[i]CE (not 1)=goblet. DON=put on. Back of [lorr]Y
12. Notorious gangster’s problem casing Yankee plant (7)
ALYSSUM AL’S (Capone’s, it usually is)=gangster’s. SUM=problem. Containing Y=Yankee in phonetic alphabet
13. Quirky fellow ringing about money.
ECCENTRIC ERIC=random fellow. Containing CENT=money
14. Absolutely what an author would do for listeners (5)
RIGHT Homophone (for listeners) for write.
16. Bug eerie East Sussex town picked up (6-6)
CREEPY-CRAWLY CREEPY=eerie. Homophone (picked up) for CRAWLEY=Sussex town
17. Girl Ted clobbered with whip: it prevents stock going missing! (6-4)
CATTLE-GRID CAT=whip. Anagram (clobbered) of GIRL TED.
19. Tree left by old poet in my part of London (8,6)
LOMBARDY POPLAR L[eft] O[ld] BARD=poet contained in MY. POPLAR=E. London district.
22. Absent-minded detective’s distinguishing feature (8)
DISTRAIT DI’s=detective’s. TRAIT=feature.
24. Powder used in hospital (Cumbrian) (6)
TALCUM Hidden in [hospi]TAL CUM[brian].
25. Her music so confused some of the singers (10)
SEMICHORUS Anagram (confused) of HER MUSIC SO.
26. Notice girl dropping by spontaneously (2,3)
AD LIB AD=notice. LIB[by]
29. Bloomin’ tailless fish (4)
RUDD RUDD[y]=bloomin’. “Tailless” not really necessary but it is helpful,
30. Agreement worker associated with enchanting female group (8)
COVENANT COVEN (of witches) with ANT=worker.
32. People engaged by board, not impossilbe to find (9)
TRACEABLE RACE=people contained in TABLE=board.
34. Silver-tongued Conservative leaving badly organised public sale (9)
PLAUSIBLE Anagram (badly organised) of PUBLI[c] SALE omitting C=Conservative
35. Free novel initially enjoyed by fashionable young man (8)
BUCKSHEE BUCK=fashionable young man followed by SHE=novel (by H. Rider Haggard often encountered in crosswords) with E[njoyed]. It took me a while and all the checking letters before I recalled this early 20th Century piece of (?military) slang, apparently derived from the word “baksheesh” meaning bribe – in some far from obvious way.
36. Actors in musical with Eliot in a spin (4)
CAST CATS is the musical, flipping the last 2 letters of the initials of the author of the original book.
39. Cricket side everyone backs, it’s plain (5)
LLANO ON=cricket. ALL=everyone. Reversed (backs)
40. Enclosure ultimately very analytic, not in papal letter (10)
ENCYCLICAL ENC. [ver]Y (ultimately). CL[in]ICAL=analytic omitting IN
42. Muslim official once – namely one employed by Queen (6)
VIZIER VIZ.(abbrev. of videlicet)=namely. I with ER
44. Vehicles carrying lean Spanish monarchists (8)
CARLISTS CARS=vehicles containing LIST=lean
46. S Atlantic islands transformed by Canadian with thrust (7,2,5)
TRISTAN DA CUNHA Anagram (transformed) of CANADIAN THRUST. British territory about as far away from anywhere as you can get.
48. Naval officer unexpectedly hid maps in entrance to mess (10)
MIDSHIPMAN Anagram (unexpectedly) of HID MAPS IN M[ess]
49. Singer or priest turning over unfinished sculpture (5-7)
BASSO-RELIEVO BASS=singer. Or. ELI=priest. OVE[r] (unfinished and reversed)
53. Container brought back by soldiers for gunpowder constituent (5)
NITRE TIN=container reversed with RE=soldiers
54. Adverse info about old times dishonestly come by (3-6)
ILL-GOTTEN ILL=adverse. GEN=info containing TT=times
55. Weighty matter party goes over after all the others (7)
BALLAST BAL=party (Lab) reversed. LAST=after all the others. At first I thought “ball” was the party but that made nonsense of the clue so I had to re-think – although I might not have bothered if I’d not been blogging.
56. European left visitor briefly in posh quarter (10)
PORTUGUESE PORT=left. GUES[t]=visitor briefly. E=quarter.
57. Roofing requirement I’d obtain in anger (5,4)
RIDGE TILE I’D GET contained in RILE=anger
1. Wife leaves old Welsh county, going over English river (5)
CLYDE Remove the W from CLWYD and add an E on the end.
2. Old French art work capturing witch’s gullet (10)
OESOPHAGUS O+ES (French art=tu es) OPUS containing (capturing) HAG=witch
3. Murderer — one detectives found in private residence (8)
HOMICIDE I CID contained in HOME
4. Schedule mainly involves this group of Muslim scholars (5)
ULEMA Hidden in [sched]ULE MA[inly]
5. Oil producers having typical ground south of Brussels (9)
EUCALYPTI EU with anagram (ground) of TYPICAL
6. Attorney leaves Commonwealth country for scene of marriage feast (4)
CANA Remove DA (attorney) from CANADA. In the NT it’s Jesus’s first miracle where he changes the water into wine.
7. Abroad securing Irish transport route (6)
AIRWAY AWAY=abroad containing IR.
8. Publican’s aid creating agitation in Manhattan (8,6)
COCKTAIL SHAKER A Manhattan contains rye or bourbon, sweet vermouth, bitters and a glace cherry garnish. Not my cup of.
9. Extremely weird new retreat oddly, a Cumbrian lake (12)
DERWENTWATER Anagram (oddly) of W[eir]D (extremely) with NEW RETREAT.
10. Rise of first-class fellow in west African republic (7)
NIGERIA AI=first-class. REG=fellow with IN, all reversed (rise). Anyone else try for Namibia?
11. Electronic device a local court deployed, missing nothing (10)
CALCULATOR Anagram (deployed) of A LOCAL C[o]URT omitting the O
15. Returning, amend story about book consulting navigational aid (4,5)
TIDE TABLE EDIT=amend (reversed). TALE=story containing B=book. The “consulting” is a little confusing – “for” might have been simpler.
18. Pitiful way to get quote set up! (8)
PATHETIC PATH=way. CITE=quote reversed (set up)
20. Genial-sounding, taking small drink before a production (9)
MELODRAMA MELO sounds like “mellow”=genial. DRAM with A
21. First choice when low-value coins secure advert (10)
PREFERENCE PENCE containing REFER=advert.
23. Capital invested at first in unruly kid’s discharge (10)
BRATISLAVA BRAT’S=unruly kid’s containing I[nvested]. LAVA=discharge. Capital of Slovakia
27. Politician, Republican, heretic — one looking after books (9)
LIBRARIAN LIB. R. ARIAN=heretic.
28. Drink putting an end to string player’s technique (6-8)
DOUBLE-STOPPING DOUBLE=drink. STOPPING=putting an end to
31. A pound bill (or more, ultimately) for fish (8)
ALBACORE A LB=pound. AC=bill. OR [mor]E. What I know about them is written on the side of a can of tuna
33. Disbelief as regarding one’s Queen visiting shelter (12)
ASTONISHMENT AS. With ON=regarding IS=ONE’S HM=Queen all contained in TENT=shelter
34. Law enforcer‘s plan of action endlessly upset celebrity (9)
POLICEMAN POLIC[y]=plan. NAME=celebrity reversed (upset)
37. Tat a rector recycled, making sculpture perhaps (10)
TERRACOTTA Anagram (recycled) of TAT A RECTOR
38. Cull a flower, so to speak — it adds zest to the course (10)
PICCALILLI A kind of savory chutney. Sounds like (so to speak) “pick a lily”
41. Fellow required in Bury right away (9)
INSTANTER STAN= our random fellow contained in INTER=Bury
43. Clever, accepting woman as deserving love (8)
ADORABLE DORA=our random woman contained in (accepting) ABLE=clever
45. Delivered books primarily telling of 18th cent masquerade (7)
RIDOTTO RID=delivered. OT=books. T[elling] O[f] (primarily). Georgette Heyer, as so often, the best source
47. Scottish magistrate, that is. propping up cricketers bar? (6)
BAILIE BAIL=bar. I.E. DNK the magistrate but I just about knew the wicket thingie so not a hard guess with the checking letters.
50. Academics upset about conclusion of priestly council (5)
SYNOD DONS containing [priestl]Y reversed (upset). Semi &Lit. (see glossary)
51. Delete Times editorial for a start (5)
ERASE ERAS=Times. E[ditorial]
52. Sleep lightly, being nearly twelve (4)