I know that this question is already quite old, but I now implemented a new package named biomartr that can perform bulk retrieval of genomes, proteomes, cds, gff, etc. Since the actual question is "Download fungal genomes" I will provide some biomartr based examples as a reference for people who in the future search for a way to bulk download all fungal genomes from NCBI RefSeq or Genbank.

To download all fungi genomes from NCBI RefSeq, one can simply type:

# download all fungi genomes from NCBI RefSeq
biomartr::meta.retrieval(kingdom = "fungi", db = "refseq", type = "genome")

Alternatively, genomes from NCBI Genbank can be retrieved by typing:

# download all fungi genomes from NCBI Genbank
biomartr::meta.retrieval(kingdom = "fungi", db = "genbank", type = "genome")

However, you are not limited to genomes. You can also download proteomes (type = "proteome"), coding sequences (type = "CDS"), and annotation files (type = "gff").

In case you wish to download only specific subgroups of fungi genomes, you can consult the getGroups() function to obtain available subgroups:

# retrieve available subgroups for the fungi kingdom
getGroups(db = "refseq", kingdom = "fungi")

"Ascomycetes" "Basidiomycetes" "Other Fungi"

We can now choose the group "Ascomycetes" and download the genomes of all fungi species that correspond to that group by typing:

# download all fungi genomes from NCBI RefSeq that belong to the subgroup Ascomycetes
meta.retrieval(kingdom = "fungi", group = "Ascomycetes", db = "refseq", type = "genome")

For more information please consult the Metagenome Retrieval Vignette. I hope it helps.