Have a look for 5th HAA Bty RMA (8 x 3.7") and 23rd HAA Bty HK&SRA (4 x 3.7"). Both present on the War Office (WO) orbats for April 1941 and onwards. 5th HAA Bty RMA arrived in MAy 1940, 23rd HAA Bty HK&SRA who had previously been in Aden and Somaliland (see the August 1940 data) arrived a bit later. At the same time, although they are included in serveral books, the Royal Marine AA batteries are not included in the WO lists. 1st RMAA Bty was the first 'British' battery operating in Egypt (HMS Nile) and remained there until it was sent to Crete.
A couple of quotes for you to mull upon, especially the footnote from page 36....
Playfair, Official History, p.35 wrote:All this was made worse by the anti-aircraft situation. Early in 1938, in response to strong representations, the War Office had sent out an anti-aircraft brigade to Egypt consisting, of twenty-four 3-inch guns and twenty-four searchlights. But trained men were urgently needed for the rapidly expanding air defences of Great Britain, and an agreement was therefore made with the Egyptian Government by which Egyptian troops should replace the British as soon as possible, consistent with a reasonably efficient state of anti-aircraft defence.
A second RM 'heavy' battery and an RM 'light' battery arrived at the end of April 1941 and were almost immediately dispatched on to Crete too as part of MNBDO I. Neither included on WO lists.Playfair, Official History, p.36 wrote:The Chiefs of Staff were impressed by these considerations and proceeded to scrape up what they could to improve the anti-aircraft position. First, they tried unsuccessfully to coax a battery out of India. Then it was decided that four 3.7-inch guns, with their crews, from Gibraltar and eight earmarked for Malta should be sent to Alexandria, the latter to be manned by the Royal Marines. In addition, twelve light guns were allotted to Egypt and it was stipulated that six of them were to be deployed at Alexandria.
Footnote: Of the guns then in Egypt, namely, thirty-eight 3-inch, four 3.7-inch, and four light (Bofors) all were manned by Egyptians, except eight of the twenty-two guns at Alexandria. All the searchlights—24 at Alexandria and 16 at Cairo—were manned by Egyptians.
The personnel of 68 HAA Regt arrived on WS6. However, 8 of the guns they acquired arrived on Clan Campbell (part of the Tiger convoy) whilst the other 16 came out with WS7.
dryan67 wrote that HQ 51 HAA Regt arrived in Tobruk on 7 April and left again on 14 April. The orbat I have for them for the end of April shows them in Mersa Matruh fortress.