yes, I disagree with AggonyDuck in the matter of Gibraltar - I don't think a Spanish war entry is necessary. For example the Swedish military access for 2entire German divisions didn't force the Swedish to break their neutrality, even though that was at a time when Britain was stronger than it was in middle 1940 which is the current time of the Interactive. Spain can always make an official statement of "disliking the incursion" and not take part in any military action after that to show their neutrality. The thing is, if Britain declares war on Spain over the military access, and can't reach Spain with military actions, Spain will not need to make any defensive actions that could confirm and strengthen the appearance of a hostile attitude, and if they keep claiming their neutrality, and it's admitted and confirmed by German statements, then the British will be the ones to look bad if they keep claiming Spain is at war.
Gibraltar would be really useful to hold. The British high-priority convoys were after all some of the most important key convoys in the war in North Africa, for instance a huge convoy of tanks for operation crusader. The longer supply routes will not hurt oil and food supplies, but will give the British a slower reaction time to shortages of military supplies such as equipment and reinforcements. Gibraltar is also a convenient stop for convoys going around Africa. Also there's the prospect of severely damaging or sinking plenty of British ships - if we're lucky we'll even be able to take over some of the ships almost intact. There's also the prospect of being able to get submarines into the Mediterranean, and the prospect of covering the Italian fleet's flank so it can effectively put an end to British control in North Africa and the rest of the Mediterranean - perhaps with the result that the Italian fleet in return can be convinced to send some capital ships to help dealing with the British home fleet later on. After British control over the Mediterranean is lost there's also the prospect of going into the Middle east and be able to get within reach of British bases in India. Most of the advantages of holding Gibraltar aren't lost even if the British invade the Canaries in response to losing Gibraltar. Doing so will give them diplomatical problems. Since the Canaries are much further south, it'll still keep the German submarine route into the Mediterranean open. Not likely, but possibly, German air bases in Morocco could be used to bombard British positions in those islands, maybe enabling the destruction of further British fleet units. The British empire will in a matter of between a few months and a year and a half be cut off into two parts - one in South east Asia, and one in Britain. The result would be that the British will either have to give up India and the last remnants of their empire outside Britain (which would perhaps make many British more open to accepting peace if they get promises of keeping their colonies in return, or at the very least lead to a British fleet concentrated around their homelands in defense and without much possibilities for offensive anywhere), or keep sending men and equipment convoys there over extremely long supply routes, which are ideal for the German submarines to harass.