Across:
1 Consistency (PARITY) in one (-I-) all-consuming political group (party = PAR-TY) (PARITY),
4 Pay no attention to (DISCOUNT) Diana’s (DI’s = DIS-) work out – the one that relates to getting the right figure (-COUNT) (DISCOUNT),
9 Dahl is missing from dining hall? (‘Dahl’ is missing from ‘dining hall’ = iningl = LINING) Keep that under your hat! (LINING),
10 Breaks up (DISRUPTS) with detective (DS = D-S) arresting purist (purist) at random (= anagram indicator) (purist = -ISRUPT-) (DISRUPTS),
12 Menu (table = TAB-LE-) contains starters of brisket on unique (starters of ‘Brisket On Unique’ = -BOU-) hot (-H) (TABBOULEH) Mediterranean salad (TABBOULEH),
13 Elk taken out of Lake Erie (‘Elk’ taken out of ‘Lake Erie’ = aerie = AERIE) by a lofty place for the birds (AERIE),
14 Insult (CAUSE OFFENCE) accountant (CA-) at function (-USE) having nothing (O-) to do with loud (forte = -F-), local dealer in stolen goods (-FENCE) (CAUSE OFFENCE),
18 Create problem (CAUSE TROUBLE), in principle (CAUSE), for Concern (concern = TROUBLE) (CAUSE TROUBLE),
21 A signal to pick up (RADIO signal) a Dior (a Dior) dress (= anagram indicator) (a Dior = RADIO),
22 Regina (-R-) and Rita (-RITA-) Lawrence (-TE- Lawrence) in papers (ID papers = I-D) (IRRITATED) got under someone’s skin (IRRITATED),
24 Those leading teams (CAPTAINS) of participants missing trip (‘participants’ missing ‘trip’ = patcians = CAPTAINS),
25 Can be found in deli (deli) speaking (= homophone indicator) (‘deli’ = ‘Delhi’ = INDIAN) to dishy type (dishy type = INDIAN meal).
26 Works in an educational institute sending children home (SUSPENDS) to America? (US) Going back (= reverse indicator) (US = SU-), uses up hard earned cash! (-SPENDS) (SUSPENDS),
27 Producers (CAUSES) opening both 14 and 18 across (opening ‘cause offence and ‘cause trouble’ = CAUSES).
Down:
1 New (= anagram indicator) topics (topics = PO-TICS) about large (-L-) unit (-I-) (POLITICS) of the housework? (POLITICS = work in The House),
2 What the promoters could do in Ring (run a boxing bout = run a bout = RUNABOUT) with small vehicle (RUNABOUT),
3 What one who’s good on their feet might be doing (TANGO) in Spartan government (in ‘sparTAN GOvernment’ = TANGO),
5 Dogs (IRISH SETTERS) people like me? (setters of crosswords / IRISH SETTERS),
6 Fish (CARP-) and chips, cheeseburgers, including oyster starters (‘And Chips Cheeseburgers Including Oyster’ starters = -ACCIO) (CARPACCIO) with thin slices of fish (CARPACCIO),
7 Sends off unimpressed (‘sends’ off ‘unimpressed’ = uimpre = UMPIRE) by the man in the middle (UMPIRE),
8 It’s a sample (TESTER) from street (street) cook (= anagram indicator) (street = TESTER),
11 Medieval (OLD-FASHIONED) cocktail? (whiskey, sugar cube, Angostura bitters = cocktail = OLD-FASHIONED),
15 Engineering (E-) on third floor (third ‘flOor’ = -O-) in Alberta (Alberta) building (= anagram indicator) (Alberta = -LAB-RATE) (ELABORATE) complex (ELABORATE),
16 Avoids (ABSTAINS) note (music not A-) from a follower (‘a’ follower = -B-) taken to the cleaners (-STAINS) (ABSTAINS),
17 They’re produced by those trading on futures (READINGS) with interpretations of advance information (READINGS),
19 Those employed by The Masons (BRICKS) embedded in The House (BRICKS),
20 Transforms (ADAPTS) fresh (= anagram indicator) tapas (tapas = A-APTS) around Dublin (-D-) (ADAPTS),
23 Dance (= anagram indicator) tango (tango = TONGA) in friendly islands (‘Friendly Islands’ = TONGA).