... I have a
simple email list of 4000 addresses (List A) and some are no good.
I've made a separate list (List B) of those bad email addresses and
want to delete all of them from the initial list (List A). Is there a
way of doing this without doing it manually? ...

Here's one way, with the original list in column A of Sheet1 and the "bad"
list in column A of Sheet2.

In cell B1 of Sheet1 put
=COUNTIF(Sheet2!A:A,A1)0
Extend B1 down to the lend of the list.

Select Sheet1 column B and use
Data Filter AutoFilter
A pull-down will appear at the top of the column.

In the pull-down select "TRUE" -- only the "bad" addresses will be visible
now.

Use ctrl-A to select all.

Use
Edit Delete

Finally, delete column B.