A total of 3147 operations took place from April 1, 2012 to February 23 this year, against 2782 the previous year.
However, "more must be done" to increase the pool of donors, improve consent rates amongst families and make better use of donated organs, according to Sally Johnston, director of organ donation for NHS Blood and Transplant (NHSBT).
About 1000 people die every year waiting for a transplant.
Rates for heart and lung transplants, she said, in particular, remained "poor", compared with international figures.
The latest transplant figures were released at the annual conference of the British Transplantation Society in Glasgow, which brought together more than 400 delegates including doctors, nurses and transplant teams.
Ms Johnston said NHSBT would be monitoring the results of the change in Wales to a system of presumed consent for donation, known as an opt-out policy, due to begin in December 2015.
The Evening Times is campaigning for a similar change in Scotland.
Last month the Petitions Committee agreed to bid for a full debate in Parliament on the issue and urged the Scottish Government to move faster on a possible change.
A UK campaign will also start this month to address public attitudes to donation. Ms Johnson said the goal was to create a society that would be "proud" to donate.
She said: "One area we know presents problems has been the UK's propensity to consent for donation. It's a stubborn and frustrating area for everyone involved. Most people think it is a good thing in abstract terms or for other people.
"For some families it comes as a surprise that their loved one was on the register because they have not talked about it. Getting people to talk is going to be key."
The BMA believes a shift to an opt-out policy will lead to greater clarity for families, because they will have been given the chance to opt out of the register. The change, it has said, would also create far greater public awareness about the issue and the wishes of loved ones.
Ms Johnston said research was carried out with the DVLA to find out which questions might prompt more people to consider become a donor.
One of the questions that provoked the strongest reaction was, "Would you be prepared to take an organ, if you would not be prepared to give one?"
She said lessons could be learned from Spain, which uses more organs from older donors.
"The rate of organ donation is 35.1 per million population, compared with 18.5 across the UK.
"The number of living kidney donations is continuing to rise - one of the highest rates in Europe - and 10% of all donations are from altruistic donors.