I'll attempt to answer this in accordance with the meta post How should unfalsifiable claims be handled?.
Bobson pointed out an interesting article from The Telegraph entitled "Starlite, the nuclear blast-defying plastic that could change the world." The article heavily relies on Ward's metaphorical testimony on the issue, and does not cite sources, although it appears to be comprehensive. All quotes here are from that article unless otherwise stated.
The article claims that three tests were made by reliable government bodies, two in Britain and one in the United States. I have not been able to confirm that any ever took place.
The article says in several places that the British military was doing tests on the material. Apparently,
The defence establishment was watching. In July that year, Ward was invited to the British Atomic Weapons Establishment at Foulness, and the egg went nuclear.
Well, then, the AWE should have some information on it, right? Well, their website is rather user-friendly. However, a search for "starlite" turns up empty. However, they have a document library . . . which is also full of null results. In that library, there is a pdf for historical documents. It lists various types of files that may be released. The supposed tests were in 1990; there are only a handful of file types that cover that year, and none are to be found.
There was another series of tests done in 1993 at a different location:
In tests at the Royal Signals and Radar Establishment in Malvern, Starlite was pulsed with lasers that would normally have burned through polymer. Instead, as Pohling-Brown reported in a widely-read article in International Defence Review in 1993, 'Starlite showed little damage to the surface, merely small pits with the approximate diameter of the beam and with little evidence of melting.'
However, according to Wikipedia, RSRE no longer existed in 1993. At that point, it became part of the Defence Research Agency. The British National Archives supposedly have records of the RSRE. However, those only lead up to 1991. After that, no information is accessible.
The DRA does not appear to have a public website, so next I went to the Ministry of Defence. A search for "starlite" yielded one article featuring the word "starlit." Not promising.
I then tried International Defence Review. Another search for "starlite" turned up only results for something else named "starlite." Furthermore, the magazine is not peer-reviewed, and the article would not have been written by those who actually carried out the tests. I sincerely doubt its reliability.
Now, there could very well be classified records of the experiments. Yet in the article, Ward said,
'They'd been trying to get something to withstand a nuclear flash for 45 years, and we did it in five minutes.' Ward was reluctant to take part at first. 'I was happy with my egg. It was just a challenge and I didn't want to lose.' This was a different league. Starlite-coated eggs were subjected to light-energy sources that simulated a nuclear flash, equivalent to a temperature of 10,000 C. 'They did it twice and it was still there. Charred, but intact.' The Foulness equipment couldn't keep up. 'I said to one scientist, "Are we doing all right?", and he burst out laughing. He said, "Normally, we do a test every couple of hours because we have to wait for it to cool down. We're doing it every 10 minutes, and it's sat there laughing at us."'
If the project was so top-secret, there's no way Ward would have been allowed to tell anyone that; The Telegraph would not have been allowed to publish - I'm guessing.
Ward also talks about Professor Keith Lewis, who was involved in some of the tests and reportedly told Ward "that it [starlite] does all sorts of things." I have not been able to find anything on Lewis - his university affiliation, his government involvement, or any other details. Searches for the quote lead back to this article.
Apparently, NASA was involved:
In June 1991, a sample was sent to White Sands atomic weapons testing site in New Mexico, in the care of the SAS, and subjected to a simulated nuclear onslaught. 'It was classed as the biggest bang in town. I've seen a video [on which] it shredded forest to sawdust, rolled some tanks around, stripped an aircraft into pieces.'
Even more interestingly,
spokesman Rudi Narangor revealing that 'We have done a lot of evaluation and … we know all the tremendous possibilities that this material has.'
The quote has nothing to back it up. A search on NASA for "Narangor" yields nothing . . . because the name is actually "Naranjor." Searches for this turn of no results. I'm inclined to believe that if the test ever took place, the results are classified . . . which doesn't explain Naranjor and his quote.
P_s pointed out a document request made to NASA by Michael Anthony Greshko. In it, he asks for documents relating to starlite, Ward and Naranjor. In return, he received two replies from Judi Hoolingsworth.
The first includes this:
Unfortunately, Rudi Naranjor is no longer employed by NASA and Headquarters email records from either time period you requested do not exist.
The second is along the same lines. No documents related to Naranjor or that supposed test are accessible to the public. This, though appears to be Naranjo, but the page is "In Memory of a friend."
I am by no means an expert, and so just because I was unable to find anything doesn't mean that it doesn't exist. But there is nothing in the public records of any of the agencies that supposedly tested starlite, which is suspicious. I would actually be very surprised if anything about those tests in The Telegraph was true, because it seems ridiculous that governments would allow something as valuable as this become public. But that's merely opinion. The facts seem to be nonexistent here, and so it appears that starlite has not been tested by a reliable independent, outside source, or that any of the claims made by Ward in the article are true.
The claim about the AWE laser test seemed at first to be referring to their Orion laser facility. The article claims that starlite was tested at 10,000 degrees Celsius. Orion has a capacity of 10 million degrees (I'm guessing that's in Celsius, too, but that's huge on any scale). However, the AWE also mentions the HELEN laser, which was operational for 25 years and was possibly used in the experiment described. Indeed, this paper from 1996 indicates that HELEN was operational in 1991 and was most likely the one used. This notes that HELEN can achieve temperatures in excess of 100eV, which, using this conversion, is well over 10,000 degrees Celsius. It appears, therefore, that the claimed temperature was achievable.
I have yet to find information about the alleged RSRE laser.