Mike,
Your pictured black jack looks to be later 1960 XK150 version, so maybe a good swap for a more correct 1953 Red painted SMITHS STEVENSON jack as per my earlier photos.
Your list of XK120 tools is just to simplistic for me to make any sensible comment, as like the Jack, there are many variations of all tools, most wrong, occasionally correct, especially if sourced one at a time from on-line market-places, such as eBay. There are very regular and ongoing misrepresented offerings on eBay, and a few serial offenders who clearly make a huge profit selling junk for good money.
But again all of this must be kept in context - not everyone needs to have 100% correct tools, and many people are just happy enough to impress their neighbours, and don’t need to make the effort and cost to be a ‘correct’ tool-kit.
If you do want exact advice regarding all your listed tools, then best to send me photos, and best to do so direct to rogerpayne@bigblue.net.au as this can involve a little back and forward, as although I can usually identify tools exactly in a good photo, some may require follow up questions.
For instance, from your listing:-
9. Schrader Valve Cap tin. Not required, were never included in XK120 tool-kit.
11. Tyre Pressure Gauge. Not required, were never included in XK120 tool-kit.
3,5. Unlikely to be correct ‘short’ SUPERSLIMS as they have BRITISH MADE on them, and not MADE IN ENGLAND as do the common ‘long’ variety, and there are THREE of these required, not just two as you list.
4,6. Unlikely to be correct SNAIL spanners for 1953, as the size markings you quote are not as they should be in 1953.
12. You should have SEVEN box-spanners, a set-of-three BSF sizes that nest-inside-each other, a set-of-three nesting AF sizes, and a single-ended 1/2"BSF Plug box spanner. You list only four, without commenting whether correct ones or not anyway.
But you get the point - each individual tool needs to be looked at and commented on its merits, or otherwise.
If you refer to Philip Porters Revised 3rd Edition of ORIGINAL JAGUAR XK book, I fully detail/photograph all XK tool-kits, so would be enough to detail what you should be looking for in a 1953 XK120 Tool-Kit.