Is there an English idiom for 'your silence implies your consent'?

I am not sure this qualifies as an idiom, but is a common enough expression: I would express it "unless I hear otherwise".

Unless I hear otherwise, I am going to leave at 4:00.

Speak now or forever hold your peace.

There is a legal phrase 'silence is acquiescence', which I have seen used somewhat in business.

The trick, in business, is to soften it a bit to show that it is trying to spare someone from being obliged to reply (to an email, for example).

I have used this, as an example:

Dear team,

I propose that we reboot the server in 5 minutes.

No reply necessary. Silence is acquiescence.

It's possible that the word you're looking for is tacit, which means to be understood or implied without being stated.