I must have missed something.
Whether you can or do apply for Spanish or Portuguese nationality has nothing to do with UK Gov. web pages. As I said the UK have no problem with anyone having British nationality, plus any other. Thus your Google searches need to be with regard to Spain and/or Portugal, not UK.
Spain does have restrictions on who can retain an existing nationality when they take up Spanish nationality. It might be that as you have a parent who is Spanish you may be an exception. Whether you are or not, the fact that you take up say Spanish nationality does not affect your British status.
I have Irish and British. I still get my pension paid in UK, medical cover in Spain through DWP and retain all the rights of being British.
In your case: If you take Spanish nationality, as I said, Spain say in most cases one must renounce their other nationality. Many people I understand just ‘say they have done that’ and all is fine. If one does actually renounce their British nationality, they can easily apply to have it reinstated.
Sorry but I do not know all your circumstances so even if I wanted to I cannot research your particular situation, although I have done that for several people in the past and have always found straightforward info for those situations.
At least at present Brexit has no bearing on what you may seek to do..O f course after that actually happens, it might be advantageous to have Spanish or Portuguese nationality. I was born in UK to a Northern Irish mother. Thus I had a right to (Southern) Irish nationality.
If I had not already exercised my right to an Irish passport I would certainly have done so after the Brexit referendum. I understand a significant number of Brits have done.
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