Lord Avebury, launching a report which details human rights abuses against Gypsy populations in Hungary, Poland and the Czech and Slovak republics, pointed out they would be able to enter Britain anyway when their states join the European Union next year.
"After May 1 2004 all these people will be coming here legally. Why spend all this money turning Romany asylum seekers back?" he asked. He suggested that EU member states should help attack the root causes of asylum claims.
"People should connect the influx of Romany asylum seekers with the failure of the states concerned to eliminate inequality. If countries eliminated violence and discrimination, people wouldn't be asking for asylum."
Under recent legislation, asylum seekers from accession countries - those which are soon to join the EU - can be deported without appeal, as such states are judged safe.
But those wanting to flee may not immediately be helped when their countries join the union, as free movement could still be withheld for between two and seven years, depending on national rules.
States are supposed to prove they respect minority rights before they join the EU, but Lord Avebury said member countries were failing to press accession states on the matter.
Reports by the EU's enlargement commission, he said, "do not give an adequate picture of the nature and scale of the problem".
He warned the EU against "encouraging states to sit back and relax on the commitments they have made, knowing that it's almost unthinkable the party will be spoiled by risking the timetable".
Peter Mercer, the chairman of the Roma Rights and Access to Justice in Europe organisation, said: "Roma are consistently bottom of the pile. Unless their situation improves, these states should not be accepted into the EU. The human rights record of the EU is at stake."
The parliamentary group's report says Roma have faced increased persecution since 1989 as enforced assimilation under communist regimes "gave way to increased marginalisation and social exclusion, culminating in the present situation of exclusion from mainstream education, inadequate housing within segregated ghettos, disproportionately high unemployment and racist violence".
In Hungary life expectancy for Roma is 15 years below that of the non-Roma population, and in the Czech Republic Roma children are 15 times more likely to be sent to poor-quality special schools for children with learning difficulties.
It warns that even where anti-discrimination legislation has been introduced, it can amount to little more than "window dressing".
"People say that countries have signed up to the human rights convention, as if that's enough," said Paul Stinchcombe, the Labour backbencher who founded the group. "It isn't, because these abuses are still going on."
This week a report by the New York-based Centre for Reproductive Rights revealed that many Roma women in Slovakia were being coerced into sterilisation.