The fried chicken chain says that from this week, 260 more of its restaurants will be offering a full menu, taking the number of fully operational sites to 400, including all restaurants in Ireland and Scotland.
500 restaurants, all of which are in England, are still unable to offer a full menu.
Customers on Twitter have complained of a lack of items including hash browns, sweetcorn, wraps, rice and salad, as well as chicken burgers.
A spokesperson for the brand has said that it hopes to have 98% of its restaurants offering the full menu by early May.
KFC shut nearly 700 restaurants in February after a switch from food distributor Bidvest to DHL and Quick Service Logistics (QSL) left restaurants without deliveries.
DHL blamed "operational issues" at a warehouse near Rugby it was using for deliveries nationwide.
The chain issued an apology in the form of a newspaper ad showing a photo of a chicken bucket with the KFC logo letters rearranged to read "FCK".
The brand made a U-turn in the wake of its unprecedented supply problems, renewing part of its contract with Bidvest Logistics last month.
“We are delighted to welcome KFC back to Bidvest Logistics," says Bidvest Logistics' Paul Whyte. "As the UK’s leading foodservice logistics specialist, we understand the complexities of delivering fresh chicken. KFC are a valued customer and we will provide them with a seamless return to our network.”