UK regulators have issued a warning that people who have a history of significant allergic reactions should not currently receive the Pfizer/BioNTech vaccine.
The incidents relate to two healthcare workers who suffered allergic reactions after having the vaccine yesterday but who have since recovered.
MHRA Chief Executive Dr June Raine told MPs on the Commons Health and Science Committee: "Last evening, we were looking at two case reports of allergic reactions. We know from the very extensive clinical trials that this wasn't a feature. But if we need to strengthen our advice now that we've had this experience in the vulnerable populations, the groups who've been selected as a priority, we get that advice to the field immediately."
Pfizer UK said in a statement: "We have been advised by MHRA of two yellow card reports that may be associated with allergic reaction due to administration of the COVID-19 BNT162b2 vaccine.
"As a precautionary measure, the MHRA has issued temporary guidance to the NHS while it conducts an investigation in order to fully understand each case and its causes. Pfizer and BioNTech are supporting the MHRA in the investigation.
"In the pivotal phase 3 clinical trial, this vaccine was generally well tolerated with no serious safety concerns reported by the independent Data Monitoring Committee. The trial has enrolled over 44,000 participants to date, over 42,000 of whom have received a second vaccination."
Data released by the US FDA show a small number of allergic reactions reported in both the vaccine and placebo trial groups (0.63% and 0.51%).
Commenting via the Science Media Centre, Professor Peter Openshaw, past-president of the British Society for Immunology, Imperial College London, said: "The fact that we know so soon about these two allergic reactions and that the regulator has acted on this to issue precautionary advice shows that this monitoring system is working well."
Dr Raine also told MPs "data packages for the AstraZeneca/Oxford vaccine have been arriving". She didn't commit to a date for a decision but said "work is proceeding intensively, and with great scientific rigour".
She was asked about the half dose, full dose approach that gave better results than two full doses. "Clearly we have a great interest into the possible reasons for the different doses having a different efficacy effectiveness readout. But the position is we will look at every piece of evidence."
She added: "We will be reaching a position on the basis of all completed studies and analyses. And of course, part of that will be to examine with great rigour the basis for the appropriate dosage regimen for UK people."