I found this a cheerful enough number, with intelligent and witty clues and nothing I could see that was obscure. My last two in, the mostly harmless crossing pair at 3d and 14a took my time to 2 seconds short of 17 minutes. At the time of writing, that’s a bit outside the average. I only sorted out the wordplay for 8d after submitting (it’s not hard) but I took care with everything else because I am a dutiful and conscientious contributor.
I trust lockdown is not proving too onerous: I’ve rather enjoyed binge watching Game of Thrones (which I had avoided before) and working my way backwards through Listener crosswords, valiantly trying to avoid looking up the synopses of the former and (when I get stuck) the solutions of the latter. Mostly I succeed, and today got to the last episode of GoT without knowing what was going to happen, though not much of it was a surprise.
On to my analysis, clues, definitions and SOLUTIONS marked.[(click to open)]
1 House found touring Uzbek capital (6)
1 House found touring Uzbek capital (6)
STUART The royal house, that is. Found: START, and U the capital of Uzbek (no “Where is Kazakhstan?” knowledge needed). (Either Tashkent or the Som, to save you looking them up).
5 Like rock formed from lava that’s cooled (as in cold) (8)
BASALTIC One of the longest definitions you’ll see. And in the brackets, one of the shortest bits of wordplay. BALTIC, as well as being the sea or the collection of states, is (informally and without the capital) “extremely cold”. Insert AS
9 Passionate, well-built chaps kept in check (8)
VEHEMENT Well built chaps are HE-MEN, with or without the power of Greyskull. Put in check, in this case VET
10 I'm disgusted by backtracking individual — it's all I can take! (6)
ENOUGH UGH for a representation of “I’m disgusted”, following an individual ONE reversed (backtracking)
11 Taken aboard ship, Neapolitan food for horse (10)
LIPIZZANER Trust the wordplay for the spelling of the Spanish/Austrian horses. PIZZA from Napoli, (actually the birthplace of the modern version) on board a LINER
13 Table: first of furniture items lost (4)
EATS I presume the furniture items are SEATS, from which the first (letter) is deleted.
14 Little personal responsibility (4)
BABY My last in, and a bit of a struggle. Reminiscent of pigeon a fortnight ago. Chambers has “one's pet project, invention, machine, etc; one's own responsibility”. Babies are (undeniably) little, but there is also the notion of, for example, a baby grand piano.
15 Shame about poles attached to cord being bent (10)
PROPENSITY Shame is PITY, the cord is ROPE, and poles N and S. Assemble.
18 Astonished, when teeth knocked out? (10)
GOBSMACKED Two versions, one the colloquialism, the other taking a more literal approach
20 Unexciting European, dull revolutionary (4)
TAME E(uropean) and MAT for dull, in revolutionary presentation.
21 Agreement stuffed, by the sound of it? (4)
PACT Sounds an awful lot like PACKED
23 Lock securing object in style (10)
TRENDINESS You need the TRESS from lock, the END from object, and IN as itself. Assemble.
25 Man is struggling to accept one — like himself? (6)
SIMIAN Our first anagram (struggling) du jour. MAN IS plus I from one. &lit-ish
26 Converted cabin behind pub in tower (8)
BARBICAN …and straightway our second, at least in part. CABIN’s letters “converted” after BAR for pub
28 How grass cutter's cut line of bushes (8)
HEDGEROW A grass cutter might be an EDGER, place it in HOW (in plain sight)
29 After publication, clear drawer (6)
MAGNET The publication a MAG, and clear NET, often with an extra T
2 Kid at home playing opera (3,6)
THE MIKADO An anagram (playing) of KID AT HOME. My grandfather used to enjoy singing "On a tree by a river", because it gave him licence to use the word tit, repeatedly and with emphasis, without being ticked off.
3 Useful thing bringing up branch stuck in a well (7)
AMENITY I think this is TINE, which I think of as the pointy bit on a fork, but is also a branch of an antler, surrounded by [on edit: A and] MY(!) as a representation of well(!)
4 Digit so extreme, ultimately? (3)
TOE A cheeky little &lit, the last letters of digiT sO extremE
5 Stick no label upside down (5)
BATON NO in plain sight TAB for label, joined and tipped over
6 Led, having heard a shot in race (11)
SPEARHEADED An anagram (shot) of HEARD A in SPEED for race
7 Prowler in deli, one's shoplifting (7)
LIONESS Today’s rather decent hidden, deLI ONE’S Shoplifting
8 Roof blown off house, ending in different block (5)
INGOT This time, the house is BINGO, house being an older (?) term for
legalised theft the game beloved of millions. Remove its "roof" first letter, and add T from the end of differenT
12 Nothing quicker around ultimately than crane fly? (3,8)
ZIP FASTENER ZIP one of the many synonyms for nothing, FASTER for quicker, and the last letters of thaN and cranE inserted
16 Attention-seeker beginning to kick lout (3)
OIK OI being the attention seeker, K being the beginning to Kick.
17 Property agreement invalid as I'm three! (9)
TIMESHARE A straightforward anagram (invalid) of AS I’M THREE. Amusing
19 Cruciverbalist's job getting harder (7)
SETTING Two definitions, the first undeniably in house
20 Beating champion of the century? (7)
TONKING My favourite clue. In cricket (and in other sports) a century is a TON, so the soi-disant champion would be the TON KING
22 Quick, a stay (5)
ALIVE BCP “ He will come again in glory to judge the quick and the dead”. Wordplay the terse A plus LIVE for stay as in I live/stay here
24 Pound invested in misery served up in joint (5)
ELBOW Pound here is the full LB, in WOE for misery “served up”
27 Edge: border of hat, not cap (3)
RIM the border of a hat is a BRIM, remove the “capital” first letter