VFS are not a government agency, they are the contractors who deal with the applications for UK visas and passport renewals. They check the documentation, do the biometrics and forward the application to UKVI (for visas) in Sheffield or India, and to HMPO (for passports) in Liverpool. They also have similar contracts for Australian, Canadian and (I think) Netherlands visas.
The delays in the UK are totally down to government inefficiency and cutbacks, Covid (if you believe them!) and Brexit (if you believe Remainers like me!).