We believe the feet washing should precede the Lord’s Supper. It prepares the heart to serve one another in humility and love, and thus leads to a close communion.
John 13:1-17 – Now before the feast of the passover, when Jesus knew that his hour was come that he should depart out of this world unto the Father, having loved his own which were in the world, he loved them unto the end. And supper being ended, the devil having now put into the heart of Judas Iscariot, Simon’s son, to betray him; Jesus knowing that the Father had given all things into his hands, and that he was come from God, and went to God; He riseth from supper, and laid aside his garments; and took a towel, and girded himself. After that he poureth water into a bason, and began to wash the disciples’ feet, and to wipe them with the towel wherewith he was girded. Then cometh he to Simon Peter: and Peter saith unto him, Lord, dost thou wash my feet? Jesus answered and said unto him, What I do thou knowest not now; but thou shalt know hereafter. Peter saith unto him, Thou shalt never wash my feet. Jesus answered him, If I wash thee not, thou hast no part with me. Simon Peter saith unto him, Lord, not my feet only, but also my hands and my head. Jesus saith to him, He that is washed needeth not save to wash his feet, but is clean every whit: and ye are clean, but not all. For he knew who should betray him; therefore said he, Ye are not all clean. So after he had washed their feet, and had taken his garments, and was set down again, he said unto them, Know ye what I have done to you? Ye call me Master and Lord: and ye say well; for so I am. If I then, your Lord and Master, have washed your feet; ye also ought to wash one another’s feet. For I have given you an example, that ye should do as I have done to you. Verily, verily, I say unto you, The servant is not greater than his lord; neither he that is sent greater than he that sent him. If ye know these things, happy are ye if ye do them.

“These words mean more than bodily cleanliness. Christ is still speaking of the higher cleansing as illustrated by the lower.. When Jesus girded Himself with a towel to wash the dust from their feet, He desired by that very act to wash the alienation, jealousy, and pride from their hearts. This was of far more consequence than the washing of their dusty feet. With the spirit they then had, not one of them was prepared for communion with Christ. Until brought into a state of humility and love, they were not prepared to partake of the paschal supper, or to share in the memorial service which Christ was about to institute.” – The Desire of Ages, p. 646.