I have just spent the last four years researching the Light Brigade for a book I will be publishing in the next couple of months.There was no Captain Jefferson who served in the Light Brigade during the Crimean War, much less one who rode in the Charge.
There was also a Charge of the Heavy Brigade on that day, and I have very little info on the officers in those regiments. I do know that there are only two "Jefferson"s listed in Hart's Army List 1860 which lists all the officers serving in the British Army for that year . . . and neither of them was in the cavalry. One was infantry and the other a paymaster.
If you can get access to Harts 1854 thru 1856 you should be able to check any Jeffersons who served in the British Army at that time.