Possible Clues:

• Pollarded more promising willow ...
• ... source of twigs to make baskets
• Small willow; its shoot
• More probing, rooting out name for willow
• Branch is more friendly when head leaves
• Cockney stocking-seller and basket-maker
• What's used by basket-maker, old gentleman outside back of house
• Tree lost heart? That's right!
• Train rose over Irish willow
• Source of twigs called withies