• “Au vu de” is fine when there is something to examine, but here this is not the case and I changed it for the factual “en raison de”.

(TLFi) Après examen, après consultation de quelque chose.

• “La charge” is not too specific here, as it has not been explained beforehand what it might be. I suppose you mean “an important number of applications are put to the administration and this causes a lot of additional work”, so I render “charge” more precise by substituting “demande” in its place.

• It is preferable to specify “de l’année” after “période” as it makes precise that one refers to a reccurring, seasonal situation, where the same problems are usually reoccurring.

• It is not at all usual to speak of “candidature” when applying for a place in a university as a student. “Candidature” is reserved for posts and then out of several persons that will submit their candidature only one will be chosen. Moreover, several candidatures in one single request is a much more unlikely possibility. So I suppose you are just a student and I substituted “inscription” for “candidature”.

• As you already explain why by a general reason (forte demande) you must remain consistent and not lead your reader into a reasonning where indecision is the outcome. Trying to round up what the reason is one will not be coming up with a clear one. “Au vu de” already means “because of”, so it is a little bit as if you were were saying “because of” twice and you need to introduce a hierarchy in your causes. This I do by adding that in your case the particular problem was the lack of rooms.

• Rather than consider the question of the availability of rooms from the point of view of their not being free, usually one does the opposite; however your formulation is still acceptable.

After the indicated modifications we can use the following proper formulation.

En raison de la forte demande à laquelle font face les cités universitaires en cette période de l’année ma demande d’inscription n’a pas été acceptée, la cause précise étant le manque de chambres disponibles.