The label that we know as Columbia in the US was CBS in England. The older, pre-1948 Columbia Records was part of EMI in the UK, hence the older Columbia label. UK EMI Columbia used the logo with the two 16th notes well into the 1960s if not later.
Are you familiar with Frank's Columbia album Swing and Dance With Frank Sinatra from 1950? It sounds in some ways like a precursor to what he would do at Capitol, but he's not really there yet, not fully formed. Frankie Laine seems much more in his element doing this kind of stuff than Sinatra did concurrently. A few years and one record label later, though, that would change, at least to these ears.