The faked clip mentioned by the OP is probably this "trailer", which created a myth:
A third Dalek film starring Peter Cushing, based on DW: The Chase and
titled Daleks vs. Mechons, was filmed but subsequently lost in a fire.
A trailer was discovered in the basement of a church in northern
England in 2009. (The supposed "trailer" was fanmade, as the graphics
were too advanced for circa 1967. Although a third film was planned as
an adaptation of The Chase, it was shelved with no work done following
the second movie's failure at the box office.)
AARU productions had the rights to make a third film, and were going to base it on The Chase, but it was "abandoned following the poor box office reception of the second film", according to
Wikipedia's entry Dr. Who (Dalek films), which references The Official Doctor Who & the Daleks Book by John Peel and Terry Nation.
(Another Wikipedia entry says that the film was to be called Daleks vs. Mechons
according to Doctor Who Magazine issue 461, July 2013. They might have got that title wrong, because the fake clip was uploaded in 2010 and I haven't found any earlier source confirming it.)
I have Doctor Who: 25 Glorious Years by Peter Haining, which says (pp. 106-7):
Although Milton Subotsky had the rights to produce a third
Doctor Who movie, the lack of success of the second picture has so far deterred him from doing so - although Tom Baker did bring him a
project in 1975 called Doctor Who Meets Scratchman, which was based
on a completely new script that he had devised with his co-star in the
TV series, Ian Marter.
Doctor Who Meets Scratchman would have featured scarecrows "animated when a fertiliser on Earth goes horribly wrong" and also Daleks, Cybermen and Vincent Price as the villain. It was never made because "the proposed £500,000 budget couldn’t be raised", according to the Peter Cushing Association's page on Doctor Who films, which concludes:
Milton Subotsky tried in vain many times throughout the seventies and
eighties to get his third Dalek film made. So far nothing is
forthcoming. Unless you count the awful Paul McGann TV movie in 1996.
However, a company called Chaos Films Plc now owns the film rights and
we may see something yet.
A book, The Nth Doctor, is about seven other ideas for Doctor Who films that were never made.