Don't remember Profumo actually being accused of being a Soviet spy, tonyav. He slept with Keeler who was in turn sleeping with a Russian who was a senior Naval Attache at the Russian Embassy. There were suggestions that 'pillow talk' may have been passed to the Russians by Keeler. Whether any secrets were spilled during said 'pillow talk', no-one knows, but Profumo had to resign because he lied to the house when denying that he had slept with Keeler.
You suppose 6 episodes does seem a bit long but morals and standards and attitudes were so very different then that maybe time has to be given to sketching in the backgrounds of the main participants and setting the scene of a very different Britain.