Rev Mosey, whose 19-year-old daughter Helga was killed, said: "My feeling is that we have three men (judges) who, from all we have been able to discover, are not politically motivated.
As the judges announced that they would deliver their judgements on the two Libyan accused on Wednesday, British relatives said they would once again press the UK Government to announce a full public inquiry into the bombing.
Some American relatives said they were determined to proceed with a civil action against Libya and that those who ordered the bombing should be exposed.
The Reverend John Mosey, speaking on behalf of the British relatives, said: "I'm surprised the verdict is so soon but glad from a personal point of view.
"We've waited for a long time, we waited over eight years for a trial and have been out here at the trial for nearly a year."
Many of the British relatives have been willing to accept the decision of the judges but stressed that only through a public inquiry would the full facts be known.
However, that view has not been shared by some victims' relatives in the US, who have vowed to seek reparation from the Libyan Government.
Rev Mosey, whose 19-year-old daughter Helga was killed, said: "My feeling is that we have three men (judges) who, from all we have been able to discover, are not politically motivated.
"They have shown themselves to be extremely shrewd and we believe they are going to come to an honest decision based on the evidence they have heard."
He said Wednesday would be an emotional day but stressed: "It will be a relief to finally know."
Whatever the decision, the British families said they wanted to highlight the failings of the intelligence services in allowing a terrorist to place a bomb on board the plane to come under the spotlight.
They are also determined to expose the "failings" of the aviation authorities in allowing a bomb to get through airport security measures and onto the plane.
'Badly let down'
Rev Mosey said: "We want to know why it was allowed to happen, when there was so much intelligence.
"We want to know why there were so many empty seats on the plane just before Christmas and why some people were warned not to get on the plane.
"The big question is why we have been so badly let down by governments and agencies employed to protect us."
Relatives of many of the Americans who died said they would be satisfied with nothing less than a guilty verdict.
Some of those at Camp Zeist voiced fears that the speed of the verdict could indicate an acquittal.
"But I feel concerned about the speed of the verdict and fear it could mean the verdict will be the one we don't want - not guilty.
"We believe they are guilty and if they are acquitted we will continue to believe that.
"There is no question in my mind that they are guilty. I don't think there is reasonable doubt."
Mr Lowenstein told reporters: "If they are found guilty we know they didn't do it by themselves - it goes right up to the top."
American Bruce Smith, a former Pan Am pilot, lost his English-born wife Ingrid, 31, as she flew to join him for Christmas in the United States.
He said: "I thought they would be ready to give their verdict. They have had eight months to consider this and to think about the evidence.
"They would have been developing an opinion as they went along."
Mr Smith said he expected a guilty verdict but said that is "only a small step towards what should be done."
"There is lots of evidence against the Libyan Government and the blame should lie with them."
Mr Smith insisted that the Libyans on trial were at the "bottom of the chain of command" which led to the deaths of 270 people.
He said Libya must still face a civil trial for the destruction of the airliner in a case filed seven years ago in the United States.