From Farndale's Years of Defeat
Page 119: 20 Feb 1940, 104th (Essex Yeomanry) Regt RHA, under LtCol E.J. Todhunter, arrives in Haifa having travelled via Cherbourg and Marseilles. Consists of 339th and 414th Btys. Initially "horsed but soon began to mechanise." Remained in Palestine until Sept 1940 when it (along with 106 and 107 Regts RHA) moved via Ismailia to the Western Desert to prep posns in the Baggush Box (just east of Maarten Baggush)
Page 126: By then (Sept 1940) it was mechanised and equipped with 8 x 18-pr and 8 x 4.5-in how. [no note on which bty had which wpn]
Page 129: Oct 1940 at Beni Yusuf camp re-equipping. [not clear whether this is motorising, or equipping with 25-pr? Actually, in conjunction with previous comment about it already being mechanised, it probably means re-equipping with 25-pr.]
Page 211: Nov 1941, still in Tobruk garrison [and possibly, therefore, still with their old weapons?]
Page 232: ~Jan 1942, 414th Bty sent to Far East with 8 x 25-pr. [It appears, from the context, that 104 Regt - or at least 414 Bty - was in Egypt at that time refitting along with 7th Armd Bde, which of course was also sent East. According to the books index the 104th seems to have changed from being an RHA Regt to a Fd Regt at about this time. Edit: actually, this last bit looks like a typo on Farndale's part - I'm pretty sure the 104th stayed RHA throughout WWII.]
Outline listing of Regtl movements here:http://nigelef.tripod.com/regtsumm.htm#RHA
Edit: on reflection, it seems like the 104th got their 25-pr either
in Oct 1940, just prior to Op COMPASS and then used them throughout the siege of Tobruk, or
in Jan 1942 just after Op CRUSADER and therefore had 18-pr and 4.5-in throughout the siege. I've had a look in various places (principally the NZ OHs and Pitt) to no avail. I expect, though, you'd be able to figure it out with a detailed book on either Tobruk and the siege, or one on Crusader - perhaps the relevant Playfair and Molony?
would be it arrived in Palestine with horses and wooden-wheeled 18-pr, motorised and obtained pneumatically tyred 18-pr and 4.5-in during 1940, then in Oct 1940 it got 25-pr and all the paraphenalia of a 25-pr regt such as quads, limbers, etc.