Set 159 was created in 7/67, the month that steam exited (9/7/67 was the final day), therefore the date of the picture must be sometime in the first week of July 1967 (light pacific 34052 was withdrawn in July 1967, one of the last to go). The train is standing in the down main platform at Eastleigh, BTW.
Unfortunately there were 43 42 'new' sets* created in July 1967, most of which had two BSKs, so the identity of the rear BSK is open to correction. Enlarging the picture, the running number of the one branded with set 159 is too indistinct so it may be either of 34281 or 34282.
At that time there were still definitely 61 Bulleid CKs on the books, plus another 21 that were recorded as being withdrawn during July 1967. So unless there is a definite record of the exact consist of that specific train somewhere, we're on to a loser...
*The sets concerned were 11-19, 51-54, 67-69, 91, 105-109, 115/116, 125/126, 130-132, 145, 150, 155-160, 170/171, 180, 185/186, 195.
EDIT: correct details of 'new' sets.