My OH has seen neurologists for decades as he has had epilepsy since a child, although he has more recently started with cognitive decline. In my experience I would say that most neurologists are pretty clueless about dementia and would not be able to offer support - there are some notable exceptions, though. Usually, in England diagnosis is made by the memory clinic and Im not sure what speciality the doctors have. It might be worth finding out who is involved in your memory clinic and asking for an appointment with the consultant. Whoever you go for, though, make sure that they specialise in cognitive problems and dementia of all types.
Mind you, if your dad has never been seen in the memory clinic, you could ask for a referral there. Everyone is entitled to a second opinion and you may not have to pay for that.