Evans, who was named as the new regular Friday night host of the BBC consumer show last April, presents his first edition with Alex Jones tomorrow.
However by late yesterday, producers had still not booked any celebrities to appear on his debut edition, leading to frantic last-minute calls to agents and PR companies, reports The Sun.
One agent said: "They've known for months that Chris Evans will be hosting the show this Friday. So we were quite surprised they were asking so late in the day if we had anyone who could appear on the show.
"Getting people at short notice in summer is tricky, so it was pretty odd for them to be getting their begging bowl out like that."
A One Show insider, who described the situation as "tense", said: "It was getting hairy. We were running out of time. Chris's first show was looking like being a disaster."
Doctor Who actors Smith and Gillan have now apparently rescued producers by agreeing to appear on Friday night's edition.
> Chris Evans 'to earn £12k per One Show'