There were 6 British Empire and Commonwealth (BEC) divisions in the Mediterranean and Middle East when Italy declared war. However, they were all under-strength.
- 7th Armoured Division formed in Egypt before World War II in Egypt as the Mobile Division. At the outbreak of war it was re-designated the Armoured Division (Egypt) and on 19/02/40 the 7th Armoured Division.
- 1st Cavalry Division formed in the UK on 31/10/39. It was at sea between 23/01/40 and 30/01/40. It disembarked in Palestine on 31/01/40. On 01/08/41 it was re-designated the 10th Armoured Division.
- 6th Infantry Division formed in Egypt by re-designating 7th Infantry Division. On 17/06/1940 the Divisional Headquarters was re-designated HQ Western Desert Force. The 6th Infantry Division was re-formed in Egypt on 17/02/41. It was re-designated 70th Infantry Division on 10/10/41.
- 6th Australian Division. The division was in Palestine when Italy declared war with two brigades. It seems to have been brought to full strength by the end of September 1940.
- 4th Indian Division. The division was in Egypt when Italy declared war with 2 brigades. It looks as if it was brought to full strength in September 1940 by incorporating a brigade from the 5th Indian Division. After Operation Compass the division was sent to The Sudan.
- 2nd New Zealand Division. The division was in Egypt when Italy declared war with one brigade. It seems to have been brought to full strength by the end of September 1940.
Another 7 divisions were either formed in the Middle East or arrived there between July 1940 and February 1941. They are arranged in what I think is the chronological order of their arrival in the Middle East or formation.
- 2nd (African) Division was formed in East Africa on 19/07/1940. It was re-designated the 12th (Africa) Division on 24/11/1940.
- 1st (African) Division was formed in East Africa on 24/07/1940. It was re-designed the 11th (Africa) Division on 24/11/1940.
- 5th Indian Division. The division (less one brigade) disembarked at Port Sudan in September 1940. It was brought to full strength by absorbing the 3 British infantry battalions in the country. Its third brigade seems to have gone to Egypt to bring the 4th Indian Division up to full strength.
- 1st South African Division. The 1st South African Brigade arrived at Mombassa in the second half of July 1940 and been expanded into a division by November 1940.
- 7th Australian Division. This division arrived sometime between 1st September 1940 and 31st December 1940.
- 9th Australian Division. I think this division arrived in January 1941.
- 2nd Armoured Division formed in the UK on 15/12/39. It was at sea between 26/10/40 and 31/12/40. It arrived in Egypt on 01/01/41. The division's headquarters was captured on 08/04/41 and the division was formally disbanded in Egypt on 10/05/1941.
I'm confident that the dates for the African and British are correct because they come from the book Orders of Battle. The dates for the Australian, Indian, New Zealand and South African divisions are as far as I can work out from the British official history of the war in the Mediterranean and Middle East on Hyperwar.
Based on that my guess is that on 28th October 1940 (the date Italy declared war on Greece) the BEC land forces in the theatre consisted of 10 divisions as follows:
6 divisions in Egypt and Palestine
7th Armoured Division
1st Cavalry Division
6th Infantry Division without a divisional headquarters
2nd New Zealand Division
4th Indian Division
6th Australian Division
1 division in The Sudan
5th Indian Division
3 divisions in East Africa
1st South African Division but without its divisional headquarters which did not arrive until November
1st Africa Division
2nd Africa Division