Exhibit 23.1 CONSENT OF INDEPENDENT ACCOUNTANTS We hereby consent to the incorporation by reference in the Registration Statement on Form S-3 (No. 333-76173) of LeukoSite, Inc. of our report dated February 12, 1999 relating to the financial statement CytoMed, Inc., which appears in the Current Report on Form 8-K/A of LeukoSite, Inc. dated February 11, 1999. /s/ PricewaterhouseCoopers LLP PRICEWATERHOUSECOOPERS LLP Boston, Massachusetts April 26, 1999