Dear Shining Light
I don't know if the info I have will assist you!
The Charles W Sadler who served in the Essex Yeomanry was a regular cavalary soldier serving pre-war: D/7629, 5th Dragoon Guards, later 1st Dragoon Guards and then 1/1st Essex Yeo. He proceeded overseas on 15 August 1914 and earned the 1914 Star and bar trio - the famous "Mons Star".
While it is just possible that he is the Charles William Sadler who was born in March 1896, note that he would have enlisted soon before the war broke out (unless he lied about his age on enlistment).
Returning to the cavalryman, he appears in a roll of regulars serving with Essex Yeo in January 1918 and is shown as HQ, 8th Cav Bde [Cavalry Brigade] 17.8.17 - which I assume to be the date he was posted to HQ, 8th Cav Bde. Finally the medal index card shows that he was discharged to class B of the Army Reserve on 7 December 1919.
Are they the same man? Possible but not certain. The unit matches. We know he had a WW1 trio. It would be interesting to see a blow up of the medal ribbons to see if we can spot the rosette on the ribbon of the star. If his service continued into the 1930s, one might expect to see a long service medal ribbon - either regular army long service & good conduct medal or perhaps an efficiency medal if he was in the TA (can anyone tell from the uniform whether he was regular or TA?). I'm not sure whether I can see a fourth ribbon but there might be one lurking there.
As for his brother, the Essex Regiment number indicates service with the 4th Bn (TF) in 1917 or later when 1/4th Bn was in Palestine. However it is common to find men with 4th Bn numbers who had proceeded via the 2/4th or 3/4th Bn to Essex R Bns serving in France. Again, one cannot be certain that they are the same man but the Middlesex link seems persuasive.
I hope this helps
Ian