Bookings opened on Saturday for children aged five to 11 in England to get a Covid-19 vaccine.
Parents and carers can arrange appointments for Monday onwards through the NHS vaccines website or by calling 119 from 7am on Saturday morning.
NHS England said hundreds of sites will offer jabs from Monday, with more coming on stream throughout the week.
Some five million children are eligible for the jab, following on from the success of the campaign to vaccinate vulnerable youngsters with health conditions.
Most new appointments will be at local vaccination centres or community pharmacies outside of school hours, and there will be walk-in clinics available, with timings on the NHS grab a jab website.
NHS England said more appointments will be added throughout the week so anyone unable to get a convenient slot should keep trying.
Children will be offered two doses of the Pfizer/BioNTech vaccine, at least 12 weeks apart, at a third of the normal strength.
Families will be given a vaccination record card with the name of the vaccine, batch number and the date the vaccine was given.
Calum Semple, professor of child health and outbreak medicine at the University of Liverpool, told Sky News: “This is now a vaccine-preventable disease and the vaccine is safer than the disease.
“It’s a very unpleasant illness for children. And if they have a weakened immune system or if they live in a family where a member has a weakened immune system, the consequences can be devastating.
“So yes I am pleased.”
Health and Social Care Secretary, Sajid Javid, said: “From Monday, the NHS will be rolling out the non-urgent offer for Covid vaccines for all children aged five to 11 in England.
“Parents, if they want, can take up the offer for their children to increase protection against Covid as we learn to live with this virus.
“Children without underlying health conditions are at low risk of serious illness from Covid and the priority remains for the NHS to offer vaccines and spring boosters to adults and vulnerable young people, as well as to catch up with other childhood immunisation programmes.”