Speaking clearly but with a slight stiffness in her upper lip, 15-year-old Malala said she was "getting better, day by day."
"Today you can see that I am alive," she said in the video.
"I can speak, I can see you, I can see everyone. It's just because of the prayers of people. Because all people - men, women, children - all of them have prayed for me," The Mirror quoted her as saying.
"And because of all these prayers God has given me this new life - a second life. And I want to serve. I want to serve the people. I want every girl, every child, to be educated. For that reason, we have organised the Malala Fund," she said.
Malala drew the world's attention when she was shot by Taliban militants on October 9 on a school bus in north-western Pakistan.
A bullet was removed from her head by surgeons in Pakistan, before she was flown to the UK for specialised treatment.
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Se underwent two successful surgeries on Saturday including one to fix a titanium plate on her skull.
Malala had been discharged as an inpatient from the hospital in January after undergoing weeks of specialist treatment.
The Queen Elizabeth is also home to the Royal Centre for Defence Medicine, which has treated many of the injured servicemen and women returning from Afghanistan.
Earlier last week, Malala was reported to have been nominated for this year's Nobel Peace Prize.