However, it seems to me that the central flaw in the theory of time travel is that any interference to the past will alter the historical record, as is shown in the Back to the Future films.
A manic time lord may indeed have meddled in history, but if he or she has altered the past, then we will be none the wiser because the historical record will have changed. The Battle of Hastings could have led to an English victory, but a Doctor Who clone may have intervened and tipped the balance of events the other way. If this is the case, then we would have no knowledge of it.
Scientists postulate an infinity of universes, each differing only slighly from the others. If this is the case, our best hope of time travel is to jump from one universe to another - one whose history suits us. Now, where's the universe in which England won THAT match?