why did they film it in black and white?

It was deliberate, somewhat avante-garde--considering how well-established Techni-Color was by then--and allegorical on several levels. In B&W the main themes become amplified, while the details are de-emphasized.

If nothing else, as several coffee-table books have since shown, B&W was excellent for showing off the Mid-Century Modernist architecture--both interior and exterior--featured throughout the film, especially Miles' home and office. So CRISP. So SHARP. The volumetric and geometric dialog so much more dominant than any of the colors or textures involved. (That post-International Style is really holding up well, and making a huge retro comeback.)

OTOH, the B&W treatment made Robert's traditional flat look extra drab and frumpy.

It depends on a definition of "notable". If you mean "artistically notable" then we might agree, given that it's a subjective judgement as to which films qualify.

I've said here and on other threads that many of the most artistically-inclined filmmakers preferred b/w.
It was often felt at the time that colour tended to be gaudy, commercial and mainly suitable for epics, musicals, adventure pics etc and b/w was better for dramatic, atmospheric, artistic or realistic subjects. (see any book which seriously asks a number of filmmakers of the period what they thought e.g. "The Making of a Feature Film" by Ivan Butler, Pelican Books 1971)

I think that which films were or were not notable is rather beside the point though. The question is whether or not filmmakers filming in Britain in 1964 (when Darling and most of the films released in 1965 were shot) made the decision to shoot in b/w solely on the basis of cost (regardless of whether the film turned out to be notable or not).

As I've said in another reply on this thread there were far cheaper films than Darling made in colour (e.g. several Amicus films) and much more expensive (including Hollywood studio-financed) films made in b/w.
Even such a commercial outfit as Hammer made films in both colour and b/w depending on the subject and feel - Their gothic horrors and adventure flicks were all colour, their psychological thrillers and dramas mainly b/w.

Even if one ignores the testimony of many film makers of the time who were quite clear about the matter, if the criterion had been almost entirely cost then you would see a fairly smooth curve on a graph with cheaper films all being made in b/w and gradually all the more expensive films in colour. That simply isn't the case.

Of course, as I've said before 1965-1966 was really the big turning point. As US TV increasingly demanded colour films (and TV sales became increasingly commercially important) then it became virtually compulsory to shoot in colour. By 1967 almost no professional feature films, at least in the English-speaking world, were being shot in b/w.
(In countries where sales to US TV were not an issue - eg behind the Iron Curtain - films continued to be made in b/w in significant numbers.)

This all points up the fact that it wasn't cost which was the primary factor as budgets weren't being significantly increased. Money was being found within existing budgets to shoot in colour. If any film with a half-decent budget in 1967 could afford to shoot in colour, so could a similar film in 1965 if it had really wanted to.
Colour was certainly more expensive to shoot than b/w but in the context of a professionally-budgetted film the difference in cost was not so significant that it was the main deciding factor.