In 2001, Parliament had already been dissolved ahead of a GE planned for May 3, when the Foot and Mouth disease crisis forced the Goverment to limit movement of people from certain areas to stop the spread of the disease. Tony Blair subsequently moved the election date to June 7.
Different situation - while Tony Blair had announced that he planned to hold the election on May 3rd, Parliament was not dissolved to set the process in motion, so no writs were issued for that date. Therefore when Blair made the decision to delay on 2nd April 2001, there was nothing constitutionally unusual about the situation. In fact, Parliament sat after that decision to pass the legislation needed to stop the local council elections that were also supposed to be held on May 3rd.
Parliament wasn't dissolved until May 14th, 2001.
It's a different situation from today when Parliament has been dissolved, and writs have been issued.