It’s the actors, not the writers, who have been advised by their union to continue working:

And per guidance from the actors guild stateside, members working under [British] Equity contracts are to “continue to report.” SAG card carriers working on Equity productions may choose to boycott but, due to tough anti-strike laws in the UK, studios would be able to sue them directly to force them back on to set.

The article doesn’t make it clear whether the WGA (the writers’ union) is advising its members to do the same on this show. Presumably it would depend on whether the writers’ contracts are struck under British or American law.