Bitcoin has been created to get rid of restrictions imposed by governments so unless the internet is completely shut down; it will still be continuous.
There are still some ways to buy Bitcoin without using banks such as paying cash to purchase gift cards "Amazon, Google Play,...etc." and then using escrow sites "localbitcoin, Paxful,...etc." to get the Bitcoins.
As long as there are people who believe in the need to reduce banks' dominance, there will still be support for the biotech that makes them strong