The article notes that they will look at other ways to hold a lawful referendum. This may mean the referendum is indicitive rather than binding. Or it could involve passing legislation with a commencement clause contingent on Westminster granting consent, waiting for it to be refused, and then going to court to try and force it to be granted (the constitutional convention with other colonies being pretty clear about that, and there being obvious reasonableness arguments. Which is probably another reason why the Tories want to gut judicial review).

It doesn't matter if this is immediately unsuccessful, because failure will just be another example of Westminster saying "no", and every time that happens support for independence rises (more time also means the demographic pressure for independence is stronger). Eventually, Westminster is going to have to agree, because a democracy cannot hold a people against their will forever - at least, not if they want to remain a democracy.

(The ultimate pathway is likely electoral - Westminster's electoral system is so cooked and gerrymandered in favour of the tories that Labour's most likely path to government is via SNP support. A referendum is the obvious price. If Labour refuses to pay it, I guess England will just face endless elections until they do)