SDLP MP Alasdair McDonnell said it would be "an absolute crime and a tragedy" if British proposals for travel between the Republic and the United Kingdom led to an attempt to set up a boundary between the Republic and Northern Ireland.
Speaking at the 35th conference of the British-Irish Inter-parliamentary Body near Oxford, Dr McDonnell said he did not want to have a passport to get from Belfast to the House of Commons.
"We must work to ensure that the freedom to travel that exists is not threatened."
Andrew Mackay, a Conservative MP, said a virtual chain could be put around these islands, so that travellers accepted by the authorities in Dublin would be accepted in London. Otherwise there could be chaos.
Another SDLP delegate, Alex Attwood, MLA, voiced fears that when a review of North-South bodies, under the St Andrews Agreement, reports next Spring, elements within unionism will try to reduce their power and influence.
He said there was danger that "new and future" unionist factions would use every opportunity to damage and diminish structures that had been so helpful.
The SDLP was also worried by the Serious Organised Crime Agency's takeover of the Assets Recovery Agency, which had been so successful in Northern Ireland. His fear was that the concentration would be on international terrorist assets and major, organised crime, taking the pressure off middle-ranking crime.
A motion was passed welcoming " the historic transformation of politics in Northern Ireland" and encouraging continuing support from the British and Irish governments as well as the US and the EU. The BIIB agreed to begin talks about the formation of an North-South parliamentary forum.