Both words are tricky.

For "Presidencia", we have to work out who it's referring to and then what to call them.
We are, I believe, in 1976, and the "Presidencia" in question is the "Presidencia de las Cortes", a position then occupied by the crucial figure of Torcuato Fernández Miranda.

"Fernández-Miranda explicará el procedimiento de urgencia
Esta tarde, en las Cortes [...]
La disposición de la Presidencia de las Cortes citada está motivada por el propósito de agilizar la tramitación de determinados proyectos de ley, así como de dar una mayor intervención al Pleno de la Cámara."
El País, 06/05/1976
http://www.elpais.com/articulo/espana/PODER_LEGISLATIVO/_COR...

Even if this referred to the "Presidente del Gobierno", we couldn't (or shouldn't) use the word "President". Mariano Rajoy is not the President of Spain, he's the Prime Minister. However, that's another story.

As for the Presidente de las Cortes, he (or she) is commonly referred to as the "President" of the Cortes in English, but to my mind that's just a lazy calque of the Spanish term. The presiding officer of an upper house (such as the US Senate) is commonly called "president" in English, but the presiding officer of a lower house, including the House of Commons or the US House of Representatives, is called the Speaker.
http://en.wikipedia.org/wiki/Speaker_(politics)

This is not just a pedantic quibble. To refer here to the "President" would obviously be misleading, because in the context of a legislature that term will normally be taken to refer to the head of state. To get round that you could say "President of the House" or "President of the Cortes", but I think it's much better to say "Speaker", which is unambiguous and creates exactly the right impression.

As for "disposición", this is best translated "order", in my opinion. "Provision" is a possibility. It is not a power held by the Speaker but an order granting him/her that power. So we shouldn't call this the Speaker's prerogative, a well-established term in itself.

Disposición is defined in the DRAE as "Precepto legal o reglamentario, deliberación, orden y mandato de la autoridad.". I think "order" is as good as anything here.