NHS Blood and Transplant (NHSBT) said blood group O negative was vital, as it could be used for patients with other blood groups in an emergency.
It said O negative blood made up 12% of transfers, although only 7% of people in the UK had that blood type.
Meanwhile, B negative blood is needed for ethnic groups.
The NHSBT said ethnic minority groups, who were more likely to have B negative blood, were more prone to sickle cell anaemia, where misshapen blood cells could block blood vessels, causing an early death.
It also said such groups were more at risk of developing thalassemia, a group of inherited blood disorders that hindered the blood's ability to carry oxygen.
Only 2% of Britain's population were B negative, but hospitals had used 6% more of this blood type in the past last four weeks than the same period last year, said the NHSBT.
B negative blood was useful as it could be used for both B negative and B positive patients, the organisation said.
Donna Batty, donor relations manager at the NHSBT, asked donors to come forward in the "next few days".
She said stocks of "these vulnerable groups" were "lower than we would like".
Ms Batty added: "We are also asking donors of those blood groups who have an appointment coming up to keep it.
"We hope our fantastic donors respond to this appeal and that they bear with us if there are slightly longer waits than normal on session as a result."
In total, 4% of the UK's population currently donate blood.
Jon Latham is assistant director of marketing of NHSBT said that ideally they wanted "first-time donors" to come forward.
He said: "The bigger the database we have for people willing to donate, the easier it us for us to call upon them at times of the year when when we have a need for a particular group."
People unsure of their blood type could find out after donating, said the NHSBT.
Those interested in donating are asked to call NHSBT on 0300 123 23 23.
People with blood groups O and B negative are being asked to donate blood, as stocks for both types have hit their lowest levels in four years.