The album was recorded in the summer of 1965. Earlier that year Paul Simon was to be heard on the BBC Light morning radio programm called “ Five to Ten ” and listeners were looking for records to buy from this singer they had heard. There was none available in the UK. So CBS England got interested in doing a record with Paul Simon.

Under the guidance of producers Reginald Warburton and Stanley West 12 songs made it to the album. The recordings came from the following 3 days: June 17, 1965, June 23, 1965 and July 5, 1965.

Many takes were done and it resulted in the use of the following takes:

from the June 17th session:
I am a rock [ Take 4 ]
Leaves that are green [ Take 11 ]
A most pecliar man [ Take 4 ]
Kathy’s song [ Take 1 ]
Patterns [ Take 3 ]

from the June 23 session:
April come she will [ Take 2 ]
The sound of silence [ Take 1 ]

from the July 5 session:
A church is burning [ Take 3 ]
He was my brother [ Take 2 ]
The side of a hill [ Take 4 ]
A simple desultory Philippic etc [ Take 1 ]
Flowers never bend with the rainfall [ Take 8 ]

The above info come from CD release of the album, which also has 2 bonus tracks, from the June 23 session:
A church is burning [ Take 4 ]
I am a rock [ Take 6 ]

As you can see a Take 4 of ‘A church is burning’ was done before Take 3, which was recorded almost 2 weeks later.
Probably there will have been more days in the studio before June 17th, when he recorded down take 11 of “Leaves that are green”. We don’t know this for sure, so we can only assume it. Just like it can be assumed that there were more session days after July 5?

A few notes about earlier recordings of some of the songs that appeared on the “Songbook” album:

Topic Records:
In [early] 1964 Paul Simon also recorded a version of ‘The Sound Of Silence‘ and ‘April Come She Will‘ for the UK label Topic Records. The songs was never used maybe because Paul Simon was under contract of Columbia and / or CBS? The planned album “New Voices” with, besides Simon, Leon Rosselson, Sydney Carter and Cyril Tawney never saw the light.

Oriole Records:
Oriole Records in the UK released a 45rpm single with Carlos Dominquez and He Was My Brother in 1964 [May 8th] as well. Not under his real name, but Jerry Landis:

This was also released [ already in 1963 ] in the US on the Tribute label [#128] using the name of Paul Kane.
If you wanted to gain in on the success in the folk-circuit, having to us other names because of earlier contracts, this would and did not help.