My spouse and daughter will be travelling together to UK.
For my kid to apply for a visa, do we need to write a separate covering letter or shall we include my daughter's details in my wife's covering Letter?
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Things work best when the consulate can 'link up' all the family members.
For a child you would use Part 7 "Travellers Under The Age of 18" and Part 9 "Remarks" of their application to include the parents' GWF numbers and/or passport numbers. It's fine to include the information in one of the parent's cover letter, but not as critical as identifying the relevant family members on the form itself.
More relevant information in this answer also.
So no, you don't need a cover letter. However your kid does need a separate application and needs to mention one or both of you as accompanying adult on their application.