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it really is a small door, at least in my limited experience of london doors. i think i've only ever lived in victorian gaffs yet our new place is decidedly "mid century" which means teeny door leading into a cavernous mid terrace house.
for me, the finish isn't all that important, tho i'd like a glass panel to let in the natural light the current door does. something sympathetic to the period would seem an obvious choice as well.
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What are the measurements?
Painted costs you in labour/materials, varnished costs you in the materials for good looking construction. Front door fitting is tricky especially in cold damp conditions as the wood on the inside is warm and dry and the outside is cold and damp, potentially leading to difficulty with the door warping. When I'm fitting doors I like to keep them at the property to acclimatise and try to fit them in the 6 months of average weather, i.e. avoid the winter and summer.
I would expect that you could get a decent door/frame etc made to measure and fitted for less than £4.5k, I think Banham do some full on security stuff for £6k. Are you specifying Banham locks, that could add £1200 in some cases.
Airhead
Your door must be a very unusual size if you can't find a door near enough to the correct size to have it cut down to fit. It's normal for a door to need cutting to fit, understandable if you really do have some kind of elfin doorway though.
What kind of finish are you looking for, painted, varnished, oiled?