Yes this is true they were invited but they were not allowed participate in the actual Victory Parade itself, the same was the story for the Polish Air Force Pilot's who were so offended that they did not attend.
The only reason for this was to not upset "Joe Stalin", and it's a sad part of our British history, but politics are politics and I suppose if they went against Russia at the time who knows what would have happened, and a possibility is that most of Europe would only now be emerging from Soviet rule.
That is very simply a lie. Free Polish forces were invited to participate in the actual Victory Parade itself. They chose not to do so and refused to accept their invitation. I suggest that you read a little history and learn more than just the lies which Polish school-children were taught to parrot by Soviet teachers.
Polish forces representing the government of Poland were also invited to participate in the actual Victory Parade itself and did not refuse to attend: they just didn't turn up.
As a matter of fact (and provable historical record) the British government under Churchill did
plan an attack against the Red Army. Check the history books.