The charity, which is under threat as the result of a government decision to cut its grant, says that abductions are likely to continue rising as the divorce rate increases and international travel becomes easier.
Reunite estimates that 1,272 children were taken out of Britain last year, usually - but not always - by their fathers in defiance of court orders. The estimated figure for 1990 is 1,192.
Many of the children will never return, lawyers say, and some will lose touch entirely with family members at home. 'These children are brought up with English culture and then whisked abroad and left wondering what the hell is going on,' Judith Bailey, a social worker with experience of child abduction cases, says.
The children are often taken to countries that have not signed agreements with Britain, leaving parents to fight lengthy, expensive and unsuccessful battles.
Orders made in British courts cut little ice, and many parents say that they receive only token help when trying to understand the complexities of foreign legal systems.
According to Reunite, it is important to prevent abductions by ensuring that police officers, lawyers and social workers are aware of the problem and able to act quickly in the event of an emergency. Too often, the issue is treated as a minor domestic matter, enabling parents to escape with the children before action is taken, the charity says.
Lawyers also criticise the Foreign Office, which they say can be lethargic when faced with the difficulty of reuniting parents and children abroad.
Some improvements have already been made. Since 1986, a total of 24 countries, including Britain, have ratified either the Hague Convention or the European Convention on child abduction. Under these agreements, children should be returned to the country from which they have been taken unless there are exceptional circumstances.
Lawyers say that the conventions usually work well, although police forces in some signatory countries are reluctant to search for abducted children, leaving the task to their parents.
However, there has been recent controversy over the extent to which the child's wishes should be taken into account. In July, the Court of Appeal accepted the wishes of a nine-year-old girl, who said she wanted to stay in Britain in defiance of a French separation agreement.
But, in an apparently similar case involving Janet Strachan, the court decided that her six-year- old son, Neil Bickford, should return to Canada even though he had said he wanted to stay in Britain. Lawyers said that the issue turned on whether judges thought children were able to make up their own minds, or were being influenced.
In this highly complex area of law, social workers say it is important that parents are helped by charities which can point them towards specialist solicitors and offer support.
Yet Reunite, the only organisation set up to help parents whose children are abducted, might have to close next year unless the Home Office overturns a decision to end a pounds 23,000 grant, which makes up 70 per cent of the charity's budget.
Lucy Jaffe, Reunite's organiser, said: 'It's a drop in the ocean for the Government, but it underpins us. Unless we get a substantial sum, the advice line and all the other support services we run will have to close.'
The Home Office said that the grant was intended to be temporary but had been extended for years, and could not continue.
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