I think the bit you're referring to as a middle eight is just the answering theme, a bit like the chorus in a song. The music goes: Bass intro, main theme, bridge, answering theme, bridge, round the loop again, end. Well, they did play it, but our collective memories are at fault, as there are so many versions. From the original theme, a variety of tweaks and edits were done to make it work as a titles theme. There are, on Vol. 1 of the Dr Who at the Radiophonic Workshop 1963-1969 CD:
Doctor Who (Original Theme) 2'21, the complete Delia Derbyshire version, quite a dry mix.
Doctor Who (Original Titles Music), 2'09 more white noise, and with a really duff audio edit in it
Doctor Who (New Opening Theme, 1967) 0'51 less intro, straight into the main theme, added 'electronic spangles.'
Doctor Who (Closing Titles), 0'41 starts with that wicked filter sweep 'scream' and mixes across to the theme, ends with the noise sweeps. The booklet in the CD says this one was unused.
The 1970-1980 CD has:
Doctor Who (Opening Titles Theme 1970) 0'46.
Lots of new reverb, ultra short version, once around the main theme, and then cuts to the end reverb and fades.
Doctor Who (Closing Titles Theme 1970) 1'13
Doctor Who (Stereo Version 1972) 2'21, which introduces the TARDIS take-off noise into the theme.
Doctor Who (Delaware Version 1972) 2'08 done on the Delaware modular synth. Nobody liked it, so it was dropped.
Doctor Who (New Theme 1980) 2'42 Modern synths take over at last, revamped by Peter Howell, ends with a sweep, and noise explosion
Everything you ever wanted to know about the original theme can be found
here.