It's all gone a bit Wibbly Wobbly

Doctor Who: Besieged (2003)

DOCTOR WHO: BESIEGED (2013)
A feature-length Doctor Who / Alien crossover fan film

The Doctor (Ryan Henderick) and his companion Ade [pronounced 'Addie'] (Natalie Clark) are summoned aboard the HMS Archer, a military research vessel in deep space, trapped by an unknown and unstoppable alien force...

Cast also includes Hamish Wilson (the 'other'' Jamie McCrimmon)

https://www.youtube.com/watch?v=_Jy4xMyZJG8 

Wha.. Who said that?

THE DOCTOR SINGS ...Pale Blue Eyes

https://www.youtube.com/watch?v=D4l2TiBV6OM

THE DOCTOR DANCES ... with a Spoon

https://www.youtube.com/watch?v=i5L5rmya3fg