I am a GP. From your description of a 'pink/ tan blob', the lesion does not sound as if it had any suspicious features when your DH first presented with it, but that may just be because you have not mentioned them here (irregular margins, irregular pigment, rapid growing, itching, bleeding, etc).
New lesions appear frequently on the skin of adults, and the vast majority are benign. If the GP documented it properly, and can demonstrate from the record that there were no suspicious features, then they did what the majority of GPs would be reasonably expected to do, and there is no case to answer. Many GPs have a low threshold for referring skin lesions now as it is often difficult to make diagnoses based on clinical examination alone.
The GP will probably also have documented the initial advice given (hopefully something along the lines of 'Come back if it itches/ bleeds/ grows further' etc).
If the lesion, when seen by a dermatologist, was biopsied as you said, rather than completely excised, then they also thought it was benign on clinical examination. (Although even when a lesion is thought benign, most dermatologists will remove the whole thing with good margins.)
Unfortunately atypical melanomas are frequently diagnosed late because they don't have the features that would lead us to suspect melanoma and have benign appearances. If we referred all benign-looking skin lesions then obviously the NHS could not cope with them, and biopsying everything would create unnecessary scarring, infections etc for patients, as well as the time, cost etc that would be involved.
From the minimal information that you have given, I suspect the GP acted completely appropriately based on the initial presentation of the lesion. In addition, unless earlier diagnosis would have changed the ultimate outcome, pursuing a legal claim is likely to be fruitless.
More importantly, is your DH OK now?