NOTE: Shameless plug for our software....
You could have a look at the SRAdb R/Bioconductor package. We pull down all the metadata from the sequence read archives at EBI, NCBI, and DDBJ and consolidate that into a SQLite file that can be used from R or any other language that has a SQLite interface.
If you are looking for non-human sequences you can use the European Nucleotide Archive at EBI. But if the papers that you are looking at, are from humans, then you need to go to the European Genotype Phenotype Archive at EBI EGA or the datatabase of Genotypes and Phenotypes at NCBI dbGaP. Be aware that despite of being public, almost all the human data from research studies are under consent agreement rules, so you need to ask for access first before able to access or use the data. Unless you want to replicate a study, it would be easy to use data from 1000 genomes or similar projects that you can download directly from the 1kg web site.
As a side note: for downloading this BIG data sets is better to use aspera than ftp when this possibility is provided (see 1kg data access)