Exhibit 23.1 CONSENT OF INDEPENDENT CERTIFIED PUBLIC ACCOUNTANTS We have issued our report dated March 23, 2001, accompanying the consolidated financial statements included in the annual report of FFP Partners, L.P. on Form 10-K for the years ended December 31, 2000 and 1999. We hereby consent to the incorporation by reference of said report in the registration statement of FFP Partners, L.P. on Form S-8 (File No. 33-73170). Grant Thornton LLP Dallas, Texas April 2, 2001