I'd love to have seen such a cross-over. Given the crew working on Season Four of Enterprise, I think they and RTD could have come up with something fun.
I'm surprised no one mentioned the time capsule from Enterprise Season One. The burned-out one that was bigger on the inside? Of course, that episode aired before there was a new Doctor Who series, otherwise I'd suspect that was intended as foreshadowing for the Christmas/Easter special.
Edit to add:
Perhaps the purists could be appeased if both shows depicted their heroes on separate missions that happen to cross paths on an alien world. Archer and crew involved in a bit of Romulan intrigue that brings them to a world that the Tardis just happens to materialize on as the Doctor is off gallivanting around time and space. Nothing major, just something viewers of either show can watch as part of their respective continuity without getting too fannish. The Doctor in the background of some Enterprise scenes, and vice-verse for the most part. Although I'd love to see Trip and T'Pol break into the Tardis.