My wife and I are both applying for a UK Standard Visitor visa.
Do we need to fill the visa application form at visa4uk separately?
That would mean we will have to go for biometric appointments separately.
Is that how it works?
Each person (including children) needs to file a separate application. Based upon your text, the recommended strategy is...
If you cannot schedule biometrics at the same time, make two different appointments but show up together and ask if they can accommodate you. No guarantees, but sometimes it works.
Note: only the primary needs to submit financial evidence. This is pointed out in the Supporting Documents Guide.
if you are applying as a family/group you do not need to provide multiple copies of the same documents
You need to apply separately at GOV.UK or VISFORUK.ORG and after you're done you register and make an appointment on the visa center's website depending on which country you're from. At that point use both GWF numbers to register for a group appointment, they will have that option on the center's website.
Hope that helps.