An influential group of MPs is to investigate claims that CIA planes have been touching down at British airfields carrying terrorist suspects.
Sir Menzies said 'scores of flights' were under suspicion
Liberal Democrat Sir Menzies Campbell said the allegation was that the CIA was moving suspects to countries where "torture may be permissible".
He said scores of flights into civilian and military airports including London, and Glasgow were under suspicion.
The EU is also calling on the US to say if it ran CIA jails in eastern Europe.
The US has refused to confirm or deny the reports, which surfaced in the US earlier this month.
A European investigator is seeking satellite images of Romania and Poland, alleged sites of the secret prisons.
Spain, Sweden and Iceland are looking into separate reports that CIA planes stopped in their territory while transporting terror suspects.
Sir Menzies, the Liberal Democrats' foreign affairs spokesman, told the BBC Five Live Breakfast that he was concerned about the allegations involving CIA planes landing at UK airports.
"If there are people being transferred in the way I've described, then it seems to me that we may well be facilitating transfer into circumstances where torture may be used and that seems to be inconsistent with our legal obligations," he said.
Meanwhile, European investigator, Swiss Senator Dick Marty, is looking into what he called the suspicious movement patterns of flights in the EU.
"This is absolutely not a crusade against America," he said.
"I think all Europeans agree with Americans that we must fight terrorism.... but this fight has to be fought by legal means," the Associated Press quoted him as saying.
"Wrongdoing only gives ammunition to both the terrorists and their sympathisers."
The UK Foreign Office has confirmed that Britain will be writing to the US, on behalf the EU, to clarify the reports of secret prisons, which were reportedly set up after the 11 September 2001 attacks.
The Washington Post newspaper first reported on 2 November that the CIA had been using Soviet-era camps in eastern Europe to detain and interrogate terror suspects.
Denials and investigations
It did not name the countries, but a day later Human Rights Watch said it had evidence indicating the CIA transported terror suspects captured in Afghanistan to Poland and Romania.
Poland and Romania have denied the allegations.
Last week, the Swedish government began an investigation to establish whether CIA prisoner flights had used Swedish airports.
Spain is investigating similar claims about secret flights from Majorca while Iceland says it has asked the US for an explanation and is still awaiting a satisfactory answer.
The CIA's controversial "extraordinary rendition" programme involves removing suspects without court approval to third party countries for interrogation.