EXHIBIT 23.1 CONSENT OF INDEPENDENT ACCOUNTANT We hereby consent to the incorporation by reference in the Registration Statement on Form S-3 (No. 33-57713) and the Registration Statements on Form S-8 (Nos. 33-31977, 33-31979, 33-51951 and 33-51953) of our report dated February 10, 1995 which appears on page F-1 of the Form 8-K of Cone Mills Corporation and subsidiaries dated March 1, 1995 with respect to their consolidated financial statements. MCGLADREY & PULLEN, LLP Greensboro, North Carolina March 1, 1995