Start with the premise that a 1953 XK120 was in fact MADE IN ENGLAND, thus typical of post-war Britain everything was 100% MADE IN ENGLAND, and to prevailing British Standards where applicable - nothing was imported (including from USA) and nothing was made to any foreign standards (including USA standards).
So all your fasteners are a mix of the historically British BSW (Coarse Threads) and BSF (Fine threads) and BA (small threads less than 3/16"), albeit mostly BSF with BA mostly in instruments/small fittings made mostly by Lucas, Wilmot Breeden, and SU. In fact there were very few BSW fittings at all. But given post-war UK was on an export priority, Jaguar was one of the first to engineer new design components in the newly developed thread system, that was an amalgam of the British Whitworth system, and the USA SAE(NF,NC) system, that was not formally introduced in a new British Standard for UNC, UNF and UNEF until 1954. So with the XK120, you start to see Jaguars/and suppliers still using BSF/BSW/BA but also introducing their best guess of the new Unified system, that was called ANC and ANF (American National Course and American National Fine). So in an XK engine you now get mostly ANF fasteners/threads and a few only ANC threads. In these smaller sizes, to all practical purposes these ANC/ANF threads are totally interchangeable with 1953/1954 onwards UNC/UNF threads (apart from the 1" ANF size - rear axle hub-nut), albeit these ANC/ANF fasteners were not made yet to agreed UNF/UNC tolerances and grades of materials. But from 1953/54 onwards, the British Standard required all bolts/setscrews made to the new UNC/UNF standard to be identified as such, and the main suppliers to Jaguar - BEES, AUTO, RO, etc did this by adding a depressed disc shape into the top of the hexagon head, thus the brand and lettering were moved to the outer still raised annulus. ANF/ANC bolts/setscrews, as well as BSW/BSF, have a flat head, and no depressed disc, with brand/lettering a little larger. This of course gets us into the idiosyncrasies of the original brands and markings and indeed a change in the grades of steel used (and thus marking on head of bolt) used on all bolts/setscrews and for 1952/54 XK120 its a real nightmare, with a diminishing mix of BSW/BSF and ANF/ANC, then an increasing use of UNC/UNF bolts/setscrews/studs/nuts used, indeed by the time you get to late 1954 XK140 there is still a few carry over stock ANF/ANC bolts/setscrews used.
So simple answer is.
For 1953 XK120 you have a mix of primarily BSF, and ANF for all your general chassis componentry, with the engine itself being made by Jaguar with ratio of earlier dominant ANF diminishing in favor of UNF, with very few ANF still seen late 1954. But anything bought in/bolted on (such as Lucas, SU components will have as per those companies used)
Same situation with ANC/UNC albeit very few actually used.
But anything bought in from other manufacturers were still mostly BSF/BSW - for instance SU carburetters, fuel pumps, and fuel lines remained BSF/BA until eventually in the 1970s started to introduce metric. British Industry, including Jaguar never liked the UNEF small thread system and stayed with BA throughout XK and E-type period, so SMITHS, LUCAS and Wilmot Breeden be aware…
If you look at a Spare Parts Catalogue, it will tell you in the decodeable part number of every fastener, whether it is BSW/BSF/BA or ANF/UNF/ANC/UNC but doesn’t differentiate ANF/UNF until the XK150 introduction of a new codeable system.
Bottom Line is you need a set of Whitworth spanners/tools, BA spanners/tools and Unified (AF) spanners/tools if you want to work on an XK120/140/150.
And when sourcing new bolts, setscrews and nuts do try and get those with the correct/original thread and dont substitute easily found UNF and UNEF threads for BSF and BA, just because you can wind them in!
And ZERO metric fasteners/threads on an XK.