Can President Trump Adjourn Congress? Yes.

Prime Minister Boris Johnson has temporarily suspended Parliament.

Is there a U.S. version of this extraordinary suspension of democracy?

Yes. 
See the U.S. Constitution, Article II, Section 3: The president “may, on extraordinary occasions, convene both Houses, or either of them, and in case of disagreement between them, with respect to the time of adjournment, he may adjourn them to such time as he shall think proper.”

Harry Truman was the most recent president to use this power—in his case to force them back into session. The last time Congress was forced into session,

But how does this work for adjournment?

To tee-up this situation a president needs to have effective control of one chamber of Congress. 
President Trump and Senate Leader Mitch McConnell are closely allied.

Hypothetically, let’s imagine that pressure builds to call a major gun bill passed— or impeachment proceedings or production of his tax returns— in the House. Senate Leader McConnell could adjourn the Senate, provided he had the votes.

This would pressure Speaker Pelosi to adjourn the House—but she would not agree to do so.

Enter the president: Seizing on this discrepancy, he could “settle” the matter by adjourning the entire Congress.

To see a brief legal opinion (very readable, short, informative) that President Truman used to convene Congress, see https://www.justice.gov/file/20711/download.

There is no such legal opinion for adjourning Congress. Boris Johnson may have inspired this kind of extraordinary planning by the White House.

The bottom line is that this power is fully constitutional even though it feels profoundly undemocratic.