Exhibit 23.1 CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM We consent to the incorporation by reference in Registration Statement Nos. 33-39646, 33-39648, 33-88470, 33-88472, 333-18869, 333-70561, 333-76264 on Form S-8 and Registration Statement Nos. 333-109681 and 333-116314 on Form S-3 of our report dated September 28, 2005, relating to the financial statements of Parlex Corporation, appearing in this Annual Report on Form 10-K of Parlex Corporation for the year ended June 30, 2005. /s/ DELOITTE & TOUCHE LLP Boston, Massachusetts September 28, 2005 64