TL;DR While Assange could legally be arrested if he left the embassy, even in the case of an emergency, in reality, he probably wouldn't be arrested in that situation.
Do the standard diplomatic protections that would apply to an embassy
apply if the embassy has to evacuate due to a similar, temporary
For example, would someone who has refuge in the said embassy become
subject to arrest once they are evacuated, or would the host state be
expected under international law to extend protections to a reasonable
@Bad_Bishop accurately states the black letter law that Assange legally could be arrested in this situation and that there is no express language in the relevant treaties that covers this situation.
But, it is also true that in matters of diplomacy, a host country will not always press to limit the benefits of diplomatic immunity to its narrowest legal extent, particularly in the case of an innocent contingency like the one suggested, in order to foster good will with the hosted delegation, and to remain in good standing in diplomatic circles more generally.
So, while Assange could be legally arrested, it is unlikely that he would be in these circumstances.
For example, if Assange stayed in one of several diplomatic SUVs during the evacuation until a reassembly place is reached, and the evacuated mission did not identify which one he was in, it is unlikely that U.K. law enforcement would try to pull him out of the diplomatic vehicle to arrest him.
Similarly, the U.K. Foreign ministry would probably recognize whatever assembly place was sought by the evacuated mission as a new embassy on a temporary basis very quickly. So, some personal mansion or office building or warehouse of an expatriate or sympathizer, or even a hotel commandeered (for substantial payment to the owner) on short notice, would probably be recognized as a temporary substitute embassy in a matter of hours, under emergency circumstances, even though the relevant treaty doesn't require this treatment in so many words.
Diplomacy values honoring the spirit as well as the letter of an agreement, and reciprocity. If the U.K. pressed its advantage as a result of an innocent emergency like this one ruthlessly, it could expect similar treatment of its diplomats if some emergency disturbed one of their embassies in the future, which is something it would prefer to avoid.
This is particularly true in the U.K., in which the habit of adherence to unwritten standards in its "constitution" for centuries has had a profound impact on its political culture. U.K. politicians universally recognize that mere adherence to enacted statutes and treaties is not a complete statement of their binding obligations in political matters.