Frederick was born 17th January 1909 at number 41, Princess Rd, Kilburn, Hendon of parents Robert Bruce Alexander and Edith Millicent Alexander (nee Brice) 
In the 1911 census we see him with his parents and siblings living in 25 Salisbury Road 
In the 1921 census he isnt at home 
Wondering why a look through his military records records, on his initial attestation form: "attandance at Barnes Home School Heaton Mersey Manchester", a long way from London. 
This school in Heaton Mersey opened in 1871; a boys only Industrial School allowing it to receive 200 commited to detention by magistrates and also for voluntary cases. (source: Children's Homes website )

Could this have been where Frederick was in 1921? An internet search revealed a Fred Alaexander aged 11 and 5 months as an 'inmate' along with a Robert Alexander (aged 12 yr 9m) and we also see Robert in the 1911 census but not the 1921!
I wonder what the circumstances were for these 2 young boys to be classed as 'inmates' so far from home? Interestingly a significant number of the boys were involved with the band and I wonder if that is where Frederick gained the skills that later saw him in the army as a musician.
More research is needed to find out why and how long he was there, but by 1926 he is back in London and enlisting in the Army.