The Duke of Cambridge has opened a new hospital centre with his wife straight from working a 24-hour shift as a search-and-rescue pilot.William went without sleep after a busy night at his base at RAF Valley on Anglesey to fit in the trip to the Royal Marsden hospital in Surrey.He was joined by his wife Catherine for the opening of the new £18m Oak Centre for Children and Young People.At the start of their tour the Duke joked: \"It was a bit of an early morning.\" But he added: \"It\'s great to be here finally - we\'ve been talking about this for a while.\"William is president for the Royal Marsden - a title held by his mother, Diana, Princess of Wales until her death in 1997.It was also the scene of Diana\'s first solo engagement.The Duke had spent part of the night on a mercy mission taking a sailor from his warship off the Isle of Man to Sandhurst to see a seriously-ill relative.He was also called out to help pick up a casualty with serious head injuries in Snowdonia.William returned to his base in Wales just after 9am before travelling to the cancer unit in Sutton, south London.A spokesman for St James\'s Palace said he would have managed little, if any sleep over the last day.William and Catherine, both 29, met patients and their parents during a tour of the centre which has been built to treat day and inpatients.The couple chatted to cancer sufferer Digby Davidson, and William jokingly asked if he could join him on the bed.They then both sat either side of the 14-year-old, who has been in the unit for most of the last three months after a relapse.Catherine was also presented with a bouquet of flowers by Alice Marples, 12, a cancer patient who met the Duke two years ago.The Oak Centre is one of the largest comprehensive children\'s cancer centres in Europe, with 31 beds.It will see almost 600 inpatients and more than 5,000 day patients every year.The opening is the first time the newlyweds have been seen together recently as they continue to keep a low profile.They have deliberately kept relatively out of the public eye since their wedding in April and have only conducted a handful of royal engagements.William, a flight lieutenant, is focusing on earning a promotion to captain and his wife is getting to know various charities as she mulls over which to support.It is thought she will opt for causes she can relate to, in the same way William chose to be patron of organisations such as the Child Bereavement Charity.The bereavement charity\'s chief executive Ann Chalmers told Sky News: \"Who Kate chooses to support is generating huge interest, so I\'m sure whatever cause she associates herself with will benefit greatly.\"We feel so fortunate to have the Duke as our patron that we wouldn\'t begin to presume we could have them both.\"In 2009, Prince William supported the charity\'s Mother\'s Day campaign telling charity workers \"losing a close family member is one of the hardest experiences anyone can endure\".\"Never being able to say the word \'mummy\' again in your life sounds like a small thing. However for many, including me, it is now really just a word, hollow and evoking only memories.\"Since then the charity has helped 70% more families, taking 25% more calls to its national helpline.The Greenhouse charity, which helps underprivileged children in London through sport and performing arts, was one of the 26 chosen by the couple to benefit from their royal wedding fund.\"Funding is obviously very important, because it allows us to pay for our staff and keep doing what we do. But the attention has more importantly given us credibility\", chief executive Michael de Georgio said.\"But we wouldn\'t allow ourselves to think Kate might select us as one of her chosen patronages.\"