'The Loneliness of the Long-Distance Time Traveller' by Joanne Harris

On the point of death after absorbing a vast amount of radiation during his final encounter with the Spider Queen on Metebelis Three, the Third Doctor stumbles out of the TARDIS, searching for Sarah Jane Smith. Instead, he finds himself in an isolated Time Paradox ruled by an unknown psychic force, stuck on Saturday 8th April, and populated by people without names. Anyone disobeying the rules or showing any sign of dissent is swept up into the Gyre. Can the Doctor persuade whatever – or whoever – controls the Gyre to free the Village, before he dies of radiation poisoning?

Notes:
*Featuring the Third Doctor

*A BBC Books 'Time Trips' eBook

*Time-placing: this story occurs during Part Six of 'Planet of the Spiders'