Well-wishers are continuing to donate to a fund set up by a couple who want to take their terminally ill baby son to the United States for treatment even though hopes have been dashed.

Chris Gard and Connie Yates, who are in their 30s and come from Bedfont, want 10-month-old Charlie Gard, who suffers from a rare genetic condition and has brain damage, to undergo a therapy trial in America.

Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, said therapy proposed by a doctor in the US was experimental and would not help. They said life-support treatment should stop.

Charlie's parents had asked European court judges in Strasbourg, France, to consider their claims after judges in the High Court, Court of Appeal and Supreme Court in London ruled in favour of Great Ormond Street doctors. But Strasbourg judges on Tuesday refused to intervene.

The couple have raised nearly £1.4 million, after launching an appeal to pay for treatment in American on a GoFundMe website four months ago, and more than £300 has been donated since Strasbourg judges announced their decision.

One well-wisher donated £100 at about 7am on Wednesday and posted a message to Charlie's parents saying: "My heart goes out to you during this crucial time. Prayers are coming your way. I pray God changes the hearts of the doctors to allow Charlie to get the care he needs and deserves."

Great Ormond Street doctors say their priority is to support Charlie's parents.

A hospital spokeswoman said the European court decision marked the end of a "difficult process".

But she said there would be "no rush" to change Charlie's care.

She said there would be "careful planning and discussion".

"Our thoughts are with Charlie's parents," said the Great Ormond Street spokeswoman.

"(The) decision by the European Court of Human Rights marks the end of what has been a very difficult process and our priority is to provide every possible support to Charlie's parents as we prepare for the next steps."

She added: "There will be no rush by Great Ormond Street Hospital to change Charlie's care and any future treatment plans will involve careful planning and discussion."

A GoFundMe spokesman said officials will have discussions with Charlie's parents about what will happen to money raised if life-support treatment is withdrawn.

He said: "When the parents are ready to discuss the next steps, our team will be on hand to help."

Charlie's mother has indicated on the GoFundMe website what will happen to the money raised if they cannot take him to the US and life-support treatment ends.

''A few people have asked us what we'll do if we don't win the court case,'' she said in a statement which was posted on the website but has now been taken down.

''We have thought long and hard about it and we would set up a charity for mitochondrial depletion syndromes (there are others that are more common than Charlie's specific gene).

''We'd like to save other babies and children because these medications have been proven to work and we honestly have so much belief in them.

''If Charlie doesn't get this chance, we will make sure that other innocent babies and children will be saved.

''We would like some of it to go to research at the specific hospital that is willing to treat Charlie, and the rest will be available to help other families to get the medication that their children desperately need.

''We hope that you can all support us in making treatments available so that nobody else ever has to go through what we have.''

She has thanked ''everyone who has supported us''.

European court judges announced their decision in a statement after analysing written arguments from lawyers representing Charlie's parents.

Ms Yates, who screamed when Supreme Court justices dismissed an appeal earlier this month, told Sky News the European court ruling was "upsetting".

A European court spokeswoman said in the statement that judges had "endorsed in substance" the approach of UK judges.

She said the UK legal framework was compatible with European human rights legislation.

Lawyers representing Charlie's parents argued that the couple's human rights and Charlie's human rights were being undermined.

They said the couple's right to respect for family life was being infringed and Charlie's right to life and liberty violated.

A High Court judge in April ruled against a trip to America and in favour of Great Ormond Street doctors.

Mr Justice Francis concluded life-support treatment should end and said Charlie should be allowed to die with dignity.

Three Court of Appeal judges upheld that ruling and three Supreme Court justices dismissed a further challenge by the couple.

Mr Justice Francis made a ruling after a trial in the Family Division of the High Court in London.

He heard that Charlie, who was born on August 4 last year, has a form of mitochondrial disease, a condition which causes progressive muscle weakness and brain damage.

Specialists in the US had offered a therapy called nucleoside.