The hosts put in a stellar bowling display to restrict Sri Lanka to just 248-9 from their 50 overs, before persistent rain prevented them from completing the run chase.
After numerous interruptions, the match was eventually abandoned with England 16-1.
Earlier, Chris Woakes and Liam Plunkett each plundered three wickets, while Dinesh Chandimal, Angelo Mathews and Kusal Mendis made half centuries.
