Hull was promised 10,000 lateral flow tests, which can provide results in 30 minutes, according to Hull North Labour MP Dame Diana Johnson.
But she told the Commons on Monday that two weeks later “they have still not arrived”.
Addressing the Prime Minister, as he announced new regional measures, she said: “So when governing during a global pandemic, shouldn’t the Prime Minister focus on delivering on the ground what has already been announced, rather than grand new promises lifted from the Downing Street PR grid?”
Boris Johnson said he would “take up immediately” the point raised about Hull and “try to understand why they haven’t got the lateral flow tests she rightly wants to see”.
It comes as Mr Johnson pinned hopes of returning to normal on mass testing.
Mr Johnson said an “untried” system of a six-week surge of testing in Tier 3 areas would be launched.
Speaking to MPs he said: “There are of course many unknowns but if it works, we should be able to offer those who test negative the prospect of fewer restrictions, for example meeting up in certain places with others who also tested negative.”
He added: “Towns and regions which are engaged in community testing will have a much greater chance of easing the rules that they endure.”
It is hoped daily testing will also be able to end automatic isolation for contacts of those tested positive.
Mr Johnson said: “We will use daily testing to ease another restriction that has impinged on many lives.
“We will seek to end automatic isolation of close contacts of those found positive.
“Beginning in Liverpool later this week, contacts who are tested every day for a week will only need to isolate if they themselves test positive.
“If successful, this approach will be extended across the health system next month and to the whole of England from January.”
Mr Johnson also revealed plans to test up to two care home visitors per residents weekly, to allow them to spend time with loved ones.
Care workers, prison staff, those in food manufacturing, and those delivering tests will also be given weekly tests.
The new tier system will see more areas put into higher tiers, the PM said.
But he ruled out imposing restrictions by district rather than region or county after Conservative former minister Damian Green warned him that people will not follow the rules if they are judged to be unfair.
Mr Green said: “In the spirit of a wise constituent who told me, ‘if the Government imposes stupid rules, we’ll all stop obeying the sensible rules as well’, can I ask (Mr Johnson) that the new tiers be imposed at a local level, districts rather than counties or regions, because restrictions which people feel are unfair to their particular community will simply not be respected or obeyed – and this in itself will have a damaging effect on our long-term health.”
Mr Johnson said he “respectfully disagreed” as he praised people for following the rules and said he expects this to continue.
He added: “The disease is no respecter of borough boundaries and we have to have some regions in which to constitute the tiers that are sensible and large enough.”
There will be an additional £7bn for NHS Test and Trace, taking the overall funding provided for Test and Trace this financial year to £22bn.