I'm not sure if you still are having concerns, but this is what I know.
Spain/UK doesn't have a dual nationality treaty, but you can have both nationalities which is slightly different to be dual. Basically each country consider you theirs.
There are exceptions to this rule a) nationality transmitted from being born having one of the parents being Spanish and the other British. Basically is called "jus sanguinis " b) nationals from the Spanish ex-colonies, so pretty much all latin-american countries, Philippines, etc.
Nor the UK or Spain will ask you to renounce to a previous nationality, but if you for example are Spanish and take another nationality later on, for example British, you have 3 years to let know the consular authorities or the government that you want still keep the Spanish nationality.
If you live in the UK, and you want to register your child as Spanish, because the father is Spanish. You will need to go to the consulate, I think it is free to do it, and you will have to take with you the birth certificate, and also you will need the Passport and DNI (Spanish National Identity card) of the Spanish father to do it. You will then be given what is called a Family book, and you can organise the Spanish passport.
My advise is that you go with your partner to the consulate, in case you need something or so. Their English website is: www.maec.es/subwebs/Consulados/Londres/en/home/Paginas/home_cglondres.aspx you can always sent them an email to ask what you need for registering the birth of your child.
You also got the form and the information (Spanish) here:
www.maec.es/SUBWEBS/CONSULADOS/LONDRES/ES/MENUPPAL/SERVICIOSCONSULARES/REGISTROCIVIL/Paginas/posting_TSW.aspx#sec1
The passport cost around £18 last time I did it and last for 10 years. It use to be 5 years before, but it has been extended. The Spanish ID only can be done in Spain in the Police administration offices and you need to make the booking online. It is done in around 30 mins, and you leave with the ID. You can have it done from birth this. I think it cost less than ?10.
I hope this helps to clarify the matter.