Yes the whole story of this family is in that St Pancras admissions register, including Alfred's surname on his birth certificate, which is why I couldn't find it for years as he wasn't a Campbell.
I went to the London Metropolitan Archives and looked at all the registers in the flesh (well dust and decay) and looked at the committee minutes that aren't on Ancestry. Alfred was mentioned a few times - they paid for him to have his appendix out and to recuperate in a home. They also supplemented his wages at Plenty's:
STPBG/082/002 Boarding out committee signed minutes
At Clarendon Square, Mon 27/2/1911
Recommending –
…
(2) That Alfred Campbell (14 ½, boarded out at Speenhamland, be placed in a situation with Messrs. Plenty + Sons, Engineers, of Newbury, Berks, and that his wages be upplemented [sic] to the extent of 5s. per week for the first year, and 2s. 6d. per week for the second year.
(Arrangements have been made for this boy to continue to reside with his foster parents, and he will receive 2s. 6d. per week wages for the first year, 6s. per week for the second year, and increasing to 10s. per week after the second year).
At Clarendon Square 5th May 1913
The committee recommends –
….
That the Guardians continue to suppliment [sic] the wages of Alfred Campbell to the extent of 5/= per week for a further period of two months, the amount to be reduced to 4/= per week at the end of that time.
Amazingly well cared for, I thought.