This is correct, MPs in the UK and Members of Congress in the U.S. are trustees, not delegates. They are there to employ their best judgment on behalf of their constituents, in their best interest. That’s the theory, anyway. In practice, elected representatives tend to act as delegates, though of their party, not of their constituents. Mavericks without their own base of power tend to have short careers if they make a habit of defying the party bosses. Elected upper houses with larger constituencies tend to create that base of power, which is part of the reason you see so much gridlock in the U.S. and in countries with similar strong bicameral arrangements.
Sadly the system doesn't seem to work without political parties, yet political parties seem to be consistently breaking the system. I know we need them, but I wish we didn't.