Between April 2007 and March 2008, ChildLine answered nearly 29, 000 calls at Prestatyn and Swansea.
Even so, ChildLine said it was still unable to answer one in three calls.
ChildLine director, Delia Van Der Lenden, said the new local service has many benefits.
Rantzen said that had Childline existed in the 1950s she would have called the number for help.
Alliance Party Youth Affairs spokesperson Michael Long has welcomed ChildLine's decision to open an office in Belfast.
ChildLine said the project was important as it brought the issue of bullying out into the open.
One abuse victim who used the charity's ChildLine service said money was needed because the charity "saved lives".
He said the cash for Childline would enable it to "help even more frightened and worried young people".
The NSPCC says 4, 500 calls are made to Childline every day, but 2, 000 of them cannot be answered.
Childline founder Esther Rantzen has said she was sexually abused as a teenager.
The NSPCC, which runs a child protection helpline alongside its ChildLine service, said the former received 95, 000 calls last year.
Fiona - not her real name - from Manchester, developed a relationship with a ChildLine counsellor at the charity's Prestatyn centre.
She said the experience had made her determined to set up the counselling charity Childline, which marks its 25th anniversary this year.
The charity ChildLine is holding assemblies in every UK primary school to tell children how to stay safe in the digital age.
The cash will also help integrate There4me.com, which provides advice online under the Childline name, and to develop a text messaging service.
Help and advice is available on the ChildLine helpline number 0800 1111.
Childline is 90% funded by donations and 10% funded by the government.
Earlier this year Childline founder and television presenter Esther Rantzen said a commissioner was needed to protect young people from abuse and bullying.
The re-released song - proceeds from which are being donated to the ChildLine charity - drops to sixth place in this week's singles chart.
The appeal will also raise money for the NSPCC's well-established ChildLine service, which aims to provide direct help and advice for the victims of abuse.
Although ChildLine is associated with helping children raise concerns about abuse, the biggest single reason for children getting in touch is because of "family relationships".
The products sold were savoury pastries, cookies and cakes - including a delicious Pudsey cake, with money raised going to Children in Need and Childline.
ChildLine is a counselling service exclusively for children and young people.
The next biggest reason for contacting ChildLine is bullying - and there were substantial increases in calls about depression and mental health and problems with friends.
ChildLine said it also helped 1, 654 children who were "in crisis" to contact the ambulance service, police, social services or children's homes to get immediate help.
Claire Lilly, of children's charity the NSPCC, said there had been a sharp rise in young people contacting its Childline help service about being approached online.
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According to the charity, since its launch in October 1986, one million children have reached the comfort, advice and protection offered by ChildLine's trained volunteer counsellors.
ChildLine says its helpline took some 3, 745 calls about abuse via the internet and mobile phones last year, with most callers aged between 12 and 15.
Since ChildLine joined with the NSPCC in 2006, the helpline has been expanded and said it answers more calls from children and young people than ever before.
According to the NSPCC, bullying is one of children and young people's main concerns and accounts for a quarter of all calls to the charity's hotline ChildLine.
BBC: NEWS | UK | Education | Boost for bullying mentor scheme
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