The Lancastrian army was drawn up in the grounds of Delapre Abbey behind a prepared defence of ditch and palisade and on the face of it was in a very strong position. On the other hand they had the River Nene at their back, less than an ideal tactical situation. Presumably they were confident their defences were likely to withstand the Yorkist attack because no sensible person wants to retreat across a river in the immediate aftermath of a defeat.
The morning of 10 July was spent in fruitless negotiation. Warwick kept finding ways to ask for an interview with Henry VI and Buckingham (Lord Constable and Henry's military commander) kept finding ways of saying 'no.' Whether discussion would have achieved anything is questionable, but maybe the Lancastrian leaders feared that Henry would settle for some compromise and were confident of victory.
It is one of the curiousities of the Wars of the Roses that the side that attacked boldly tended to win over the one holding a defensive line. At two o' clock in the afternoon the Yorkists went forward in heavy rain - well, it was England in July! The Lancastrian cannons did not appreciate the weather and worked poorly and it may be that the archers' effectiveness was also reduced, as bow-strings were very vulnerable to water. (Archers usually hid their strings under their hats if marching in wet weather.)
However the key factor was the decision of Lord Grey de Ruthin, on the Lancastrian flank, to change sides. It is highly unlikely that this was a spur of the moment decision, although how exactly the defection was arranged is unknown. (I can only assure you that Alianore Audley was not involved.)
Anyway, instead of fighting Grey's men assisted the Yorkists over the ditch and stakes, and then joined them. The Lancastrian flank was thus cruelly exposed and rolled up. Within half an hour the battle was over.
Acting on orders, the Yorkist soldiers were particularly keen to hunt down and kill the enemy nobles, knights and gentlemen, while disregarding the escaping common soldiers. Buckingham, Shrewsbury, Egremont and Beaumont were all killed. Henry VI was captured in his tent and treated with due respect.
(Grey de Ruthin's grandfather, as readers of Within the Fetterlock will recall, was a strong supporter of Bolingbroke, and his mother, Constance Holland, was Henry IV's niece. It is perhaps surprising that a peer with such an impeccable Lancastrian background should defect, but he became a staunch Yorkist and was created Earl of Kent by Edward IV in 1465. He outlived the Yorkist dynasty, surviving until 1490.)