The National Mountaineering Exhibition at Rheged in Cumbria, United Kingdom has among its exhibits an ice-axe labelled as having been used by Sandy Irvine during his and Mallory's final push in 1924. However, there is no evidence that it is indeed Irvine's axe.
On 30th May 1933, Percy Wyn-Harris, a member of the British Mount Everest Expedition, found an ice-axe. In an account of the expedition published in 1934, Hugh Rutledge wrote "[The axe] was lying loose on a slab at an angle of about 30°, about 60 ft. Below the crest of the N.E. arête. The maker was Willisch of Taesch [Switzerland, J.H.]. … A number of Willisch axes were supplied to the expedition in 1924, so we cannot be certain whether this axe was being used by Mallory or by Irvine." (Ruttledge, H. "The Mount Everest Expedition, 1933, Alpine Journal, 45, 1934, p. 226)
The basis for asserting that it was Irvine's is that the axe has three small v-shaped grooves (or nicks) carved into one edge of the handle approximately one-third of the way down from the head under the curved side of the head. These are said to match the nicks carved onto a swagger-stick, found among Irvine's possesions, that dated from Irvine's days in the Officer Training Corps (now the Combined Cadet Force) at Shrewsbury School.
However, Wyn-Harris maded it clear that "When I picked up the axe there was no mark on it. The cross, over which there has been so much controversy, was not put on either by Mallory or Irvine. It was in fact cut by my personal Sherpa porter, Kusang Pugla, who did it under threats from me that it must not be lost or mixed up with other axes." (Walt Unsworth, Everest, pub 1981, Allen Lane)
Now, this is curious. Presumably, the finding of an axe in so remote a location - and the '33 expedition was the first since 1924 - coupled with the mystery and controversy that had already sprung up around Mallory and Irvine's attempts would have caused Wyn-Harris to examine the axe closely. Certainly he paid close attention to it's location. Surely, had he done so, he would have noticed the three nicks and therefore not needed to order a sherpa to mark it so as to make it unique.
Also, note the reference to "the cross, over which there has been so much controversy...". This relates to the dispute that existed since 1934 when Noel Odell in "The ice-axe found on Everest", (Alpine Journal, 46, 1934) refuted Ruttledge's assertion that the axe marked the site of a fatal fall and asserted "It seems to me very possible that one of them - and more plausibly Irvine, who was less used to carrying an axe on a rock-climb than Mallory - may have decided to leave his axe on the ridge during the ascent...".
It wasn't until 1963, that the swagger stick with three nicks was found yet not once in any literature during the intervening 33-years, was any reference made to three nicks on the ice-axe.
The ice-axe on display at Rheged does have a roughly scratched cross, so it is clearly the one that Wyn-Harris found. However, given that the axe was so unadorned that it needed to be marked and that there is no reference to three nicks before 1963, a plausible inference is that the marks were added at some point after 1934 (when the '33 expedition had returned to England). This of course does not mean that it wasn't Irvine's axe, but equally it cannot be said to be irrefutably Irvine's axe.
This may seem a minor point, but since so many of the theories around Irvine and Mallory's last day center on the location of the axe, it's significance and reason for being where it was and who was carrying it; accurate identification of the axe is important. If it was Irvine's then Irvine was in some way part of the reason why it was found where it was. If it was Mallory's, different significance must be placed on it.