The Health and Social Care Committee said it was “yet to understand” why this had not been introduced and called for it to happen as quickly as capacity allows and “certainly before winter”.
The cross-party group of MPs said staff treating patients should not be put at any “further unnecessary risk” of catching or spreading coronavirus.
In a report, they said: “The committee accepts the advice from many eminent scientists that there is a significant risk that not testing NHS staff routinely could lead to higher levels of nosocomial (hospital-acquired) infections in any second spike.
“We therefore urge the Government to set out clearly why it is yet to implement weekly testing of all NHS staff.”
MPs said the Government and NHS England must set out by the end of October what current capacity there is for testing all NHS staff, what further capacity may be needed and how long it is likely to take to offer routine testing.
Their report warned that around 70 per cent of Covid-19 carriers could be asymptomatic “and only the routine testing all healthcare staff will ensure core health and care services are returned to normal levels”.
It added: “Regular testing of NHS staff will also help to reassure the public that NHS services are safe to use.”
Health Secretary Matt Hancock told MPs on June 24 that NHS staff could expect regular surveillance testing, but this has not yet happened.
The committee said further clarification was also needed from England’s chief medical officer, Professor Chris Whitty, regarding “whether he has advised the Government to introduce routine testing of all NHS staff in the current virus hotspots and if not, why”.
Health and Social Care Committee chairman, and former health secretary, Jeremy Hunt, said: “Weekly testing of NHS staff has been repeatedly promised in hotspot areas – but is still not being delivered.
“Failure to do so creates a real risk that the NHS will be forced to retreat into being a largely Covid-only service during a second spike.”
The report also sets out failures in communication with patients about delays and cancellations to their referrals and appointments as a result of the pandemic.
“Some patients – even with life-threatening conditions such as cancer – have reported the emotional distress that has resulted from them being unclear as to when their medical appointment will take place,” the study said.