A Welsh Tory MP says the "unnecessary delay" in arranging priority supermarket deliveries for people advised to stay indoors for three months has caused "significant distress" to many of his constituents.
On Wednesday the Welsh Government announced it had agreed a deal with eight major supermarkets.
Alun Cairns criticised how long it had taken to set the scheme up.
Environment minister Lesley Griffiths has said the work was "significant".
Mr Cairns, the MP for the Vale of Glamorgan, was among a group of Welsh Conservative MPs who wrote to Welsh ministers last week expressing concern that, while in England people being advised to "shield" themselves at home had special access to food deliveries, those in Wales did not.
The Welsh Government has agreed with eight major supermarkets to give access to priority delivery slots to over 85,000 people who have medical conditions that make them especially vulnerable to Covid-19.
Those people have received a doctor's letter advising them not to leave their home for 12 weeks. This process is known as "shielding."
Officials advice those in the group to continue to rely on family and friends for shopping if possible because of the demand for priority delivery slots.
Shielded people also have the option of registering with their local authority to receive a weekly food box if they need to.
Mr Cairns criticised the length of time the arrangements have taken.
"This has been a major worry for the most vulnerable people in my constituency. The unnecessary delay has caused significant distress to many," he said.
"Why didn't the Welsh Government just follow the UK Government model? They don't always have to do it differently and we would have been served better."
Welsh Government ministers have said the delay in giving supermarkets the database of those being "shielded" was because it contained sensitive personal information.
The Environment Minister Lesley Griffiths told AMs on Wednesday it was "a significant piece of work" to negotiate data protection agreements with each supermarket.
She told a session of the Welsh Assembly: "I wanted to be absolutely sure that we weren't sharing data that we shouldn't be sharing.
"Maybe other countries are being a bit more lenient, but I have been really keen that we have to have all the i's dotted and the t's crossed in relation to sharing that data."