I've had a chance to ponder this question after my early rapid knee-jerk response.
It depends what it is about cut flowers you like: just the fact of colour in the room, the potential for showiness in arrangements (just for yourself or to brag about) or the scent aspect of flowers.
The inherent problem with cut flowers is that they die. the only real advantage is managing to cram lots into one vase or arrangement.
Before i bought this farm and lived in Sth London it wasn't worth growing much in the way of veggies in a small garden with grass for the kiddies: so i had a conservatory as a plant room and a double glazed greenhouse. While my bigger interest was in growing difficult stuff: citrus, pineapples, bananas.. I also grew some showier stuff: Orchids, other bromeliads like the urn plant, strelitzia (i left behind several huge staghorn ferns - no flowers but superb interest plants)
Now if the idea is mostly some colour then orchids..particulalry phaleonopsis give huge value for money. they're easy enough to look after, last for weeks to months in bloom and will grow bigger and more flowering spikes year on year. Cymbidium are more showy but don't flower for as long. More showy still but shorter flowering are the dendrobiums and pansy orchids. Some of the monkey orchids actually have a scent - I had one that smelt of chocolate. Out of all of them the phals are easiest.. avoid overwatering, feed little and regularly and rest between flowerings.
If you're after scents then miniature roses potted indoors and tea roses outside... roses are a bit of a ain with their common need for disease control but if you get into a routine then not so bad..specally if the aim is for indoor results.
For foliage as part of an arrangment then a baby's breath shrub in the garden will supply lots and add white dottyness when flowering.
You can also have early lilly bulbs indoors and then move them out (so long as no cats to eat them) - and the varieties are legion.. as indeed humble tulips and daffs.
Now if you really want to get showy and prepared to devote the space, time and conditions then ginger or even bananas - now they really take some space to get going
https://uk.pinterest.com/hatetheheat/flower-banana/Essentially I'm widening the remit and pointing out that flowers are flowers .. and they don't have to be cut to have indoors or grown specially for cut flowers - as simple as pot mums indoors (easy to grow and weeks of flower).
I loved my strelitzia.. you can pot-bind them to have in the house but back then mine were in dustbins dragged out of the greenhouse for the summer and dragged back for the winter - a job for a younger version of me: a dustbin of wet soil weighs seriously. It;s probably just as well that my attempt to grow a giant white failed - they can get to 20feet and a dustbin isn't quite enough
Or you can go to the really dramatic - plumeria. I started growing some from seed a couple of years ago but abandoned the project and let them take their chances overwinter unheated greenhouse (they died) because I've got enough to do. My OH won't let me have them in the sun room here.. house isn't as big as the one we had before..and illogically she hates pot plants. But plumeria are stunning and loads of varieties.. and even graftable for mixed flowers on one rootstock
http://www.plumeriasuk.com/hawaii.html