Both are correct. Both are used in BrE. I heard 'lay the table' more often growing up.

I agree with Paul, they are both used in BrE, though you'll often find there are regional preferences. For example in South Africa when I was growing up I heard "lay the table" more often, and "set the table" was a more formal older person way of speaking. This isn't the case everywhere.

Set the table is correct ! When taking things off the table we say "clear the table" :)