To begin with, it's set in the future. Written in 1896 (mostly) and published in 1898 (in novel form; it had been serialized a year earlier), its opening sets the action in the twentieth century:
"And early in the twentieth century came the great disillusionment."The narrator recounts events that happened six years in the past, during an opposition of Mars:
"The storm burst upon us six years ago now. As Mars approached opposition, Lavelle of Java set the wires of the astronomical exchange palpitating with the amazing intelligence of a huge outbreak of incandescent gas upon the planet."Although the novel doesn't explicitly say the gas flares occur the same month and year as the Martian landings, the flares happen "toward midnight of the 12th" during a warm season, the landings happen in "that terrible June," (and the Thunder Child sacrifices itself "that June morning" on day six of the invasion) and the narrator doesn't provide any indication of time passing but instead strongly implies that the ten flares almost immediately precede the landings.
The narrator speculates the cylinders travel "many thousands of miles" in a minute -- 1,000 miles per minute covers the distance from Earth to Mars (40 million miles) in about a month. If "many" = 10, in less than three days. The Martians launch one cylinder per day for ten days, and all ten launch before the first one lands, so we can assume the cylinders take at least ten days to travel from Mars to Earth. (10 days travel implies 2,770 miles per minute. 2.7 isn't my idea of "many.")
So during which opposition did the Martians launch?
"During the opposition of 1894 a great light was seen on the illuminated part of the disk, first at the Lick Observatory, then by Perrotin of Nice, and then by other observers. English readers heard of it first in the issue of Nature dated August 2. I am inclined to think that this blaze may have been the casting of the huge gun, in the vast pit sunk into their planet, from which their shots were fired at us. Peculiar markings, as yet unexplained, were seen near the site of that outbreak during the next two oppositions."The "next two oppositions" after 1894 came in 1896 and 1899. We know the landing happens "early in the twentieth century."
There is no opposition in June until 1922, although there's a May opposition in 1905, and a July opposition in 1907. Either one might work for our purposes.
The first cylinder lands on a Thursday night, probably at midnight as the later cylinders do. The Martian invasion lasts a little over three weeks. It's obviously impossible for a three-week invasion to all occur in the same month if it begins ten days after "the 12th." So the "terrible June" has to extend at least a little ways into July.
And what have we here? In 1905, ten days after "the 12th" of June, June 22, falls on a ... Thursday. Of course, remember that quote? The flare comes "as Mars approached opposition," so a May 1905 opposition is still wrong for a June 12 sighting. (The opposition was on May 8, so even if we move the landings to May, the sighting is still after the opposition.)
Also mitigating against it: the Weybridge curate says they rebuilt the church "only three years ago." There are two Anglican churches in Weybridge, neither of them rebuilt anywhere near our period. But St. Mary Oatlands, Weybridge, did in fact build a new tower in 1905 after a general period of refurbishing and restoration.
Sadly, there is no opposition in 1908, and the 1909 opposition is in September.
So what about that July 1907 opposition? If the sighting is "toward midnight of the 12th" you can put the sighting on the evening of June 11th ("as Mars approached opposition") since midnight for an astronomer marks the beginning of the next day (23:59 is June 11, midnight is June 12) but the landing has to happen more than ten days later, as the next available Thursday is June 27th. It seems unlikely that the tenth flare happens on the same night (at the same time!) as the first cylinder-fall. Yes, we'd like to pretend the Narrator doesn't explicitly say "After the tenth shot they fired no more -- at least, until the first cylinder came." But he does.
He's more likely to have been mistaken about the curate's ramblings about the new church, so we can at least put the curate's testimony down to the Narrator's foggy memory ("we built the tower only two years ago") and let the Narrator's lack of explicit time indicators from observation to landing set a sorta satisfactory date for the Martian invasion: June 28-July 20, 1907.
[Edited thanks to keen-eyed Mark Graybill, who noticed that I'd misread the 07/06/1907 opposition as a 1906 opposition, which of course threw the whole calendar thing into a cocked hat.]