In Britain you may often hear "Drop in any time. " or "Come to see me soon. ", but you can't really do that. People just say those things to make you feel welcome. It is better to telephone before visiting someone at home. If you receive a written invitation to an event that says "RSVP ", you should reply to let the person who sent the invitation know whether or not you plan to go.
You should never accept an invitation unless you really plan to go. You may refuse by saying, "Thank you for inviting me, but I will not be able to come. " If, after accepting, you are unable to go, be sure to tell those who are expecting you as soon as possible that you will not be there. Although it is not necessarily expected that you give a gift to your host, it is considered polite to do so, especially if you have been invited for a meal. Flowers, chocolate, or a small gift is all appropriate (合适的). A "thank-you " note or telephone call after the visit is also considered polite and is an appropriate way to express your appreciation for the invitation.