The storage seems odd, is it not at a shop? Have you tried going through the personal shopper or the Terminal Transfer Request? You can use this form, and you will be escorted through to the terminal in question. Either to pick up the items from the shop or other secure location airside, or to make a purchase from T4? (Which I guess you could refund, or say nah sorry not quite right).
https://boutique.heathrow.com/en/contact/contact
KF