Very little is generally known about Alfredo. In fact, at one time, it was thought by many (including myself) that Alfredo was actually Campoli, the celebrated classical violinist and conductor.

However, his real name was Alfred Gill. He was touring the halls in the early days of the 20th century as "Alfredo, the Vagabond Violinist". 

From December 1922 up until 1925, Alfredo is shown in "British Dance Bands on Record" as being a member of Jack Hylton's band. I can only say I have not seen any photographs of Hylton's band at this period which show Alfredo as a member. As Hylton organized many bands, maybe Alfredo was a member of "The Hylton Organization" but not a member of the main band?

In 1925, Alfredo formed a band of his own, to play at the New Princes restaurant. This band included sax player and vocalist Bert Bown, who had also been a member of Hylton's organization (again - I've not seen him in any Hylton photographs). The other members of the band included Arthur Wilson (trumpet), Laurie Day (piano) and Charles Harris (drums). The rest of the musicians are, as yet, unidentified, but a photograph was recently found and can be seen (top right, above). 
The band played at the New Princes for about 2 years.  

During the latter part of 1926, Alfredo re-organized the band and it now contained a fairly stable personnel right up until he disbanded in 1930. He recorded for Edison Bell from 1925 until 1930 and after the 1926 reshuffle, the band maintains the same distinctive sound right through. It was not a large band (generally a nine-piece) but they made some fine records for Winner, Electron and Radio, some of which feature fine hot solos by trumpeter Alfie Noakes (father of television's John Noakes, of "Blue Peter" fame). Some records have extra musicians added.

The Rust/Forbes discography give a bewildering mixture of differing personnels for the band, but my own opinion is that the records were made by the 'main' personnel of:
Alfie Noakes -t/ Richard McDonald -tb/ Claude Cavalotti -as/ Bert Bown -ts/ Alfredo -vn/ Frank Walsh -p/ Steve Gauna -bj-g/ Tom Eggerton -bb/ Charles Harris-d.
(Les Allen, Mark Sheridan & Ron Garrison replace Bown, Gauna & Eggerton  during 1927/28).
The other personnels given in the discographies  refer to the many other bands which Alfredo organized during this time, such as the band he put into the Park Lane Hotel in 1927 which was directed by Wilbur Blinco (this is not Jay Wilbur, despite the comment in Rust/Forbes). According to his letterhead (in an advert in 1928), he is described as "director of dance orchestras" and lists his engagements as: New Princes restaurant, Grafton Galleries club, Moss Empire theatres, Stoll theatres.

When Les Allen joins the band in 1927, it is noticable that, along with Allen, Hal Swain also contributes some vocal choruses to the band's records. Swain had his own band to run (also at the "New Princes"), so it unlikely that he was a member of Alfredo's band, he was probably present just for the recordings; he may also play saxophone on the records. Worth mentioning here is the fact that Swain, Allen, Frank Walsh & Ron Garrison had all been members of Swain's New Princes Toronto Band in 1925.

In 1931, Alfredo changed his style of music, forming a gypsy band (mainly of genuine Romanies, initially). He made a few records for HMV under the sober name of "Alfredo and his Orchestra". His right-hand man, Claude Cavalotti was a member of the gypsy band too.

Alfredo

Alfredo & his Band circa 1925-26 (photo courtesy 
Charles Hippisley-Cox)

Alfredo & his Band,
from 1926 sheet music

Alfredo and his band - late 1926 or early 1927

Alfredo & his Band  in 1927
(photo courtesy of Alasdair Fenton)

Alfredo & his Band, summer 1927

 Advert showing the versatility of the musicians (1928)

Alfredo & his Gypsy Band - circa 1933 (photo courtesy
Charles Hippisley-Cox)