I'm putting a stove in currently so have been reading Part J and my understanding is a vent pulling from under a suspended floor is fine. Its what I've done too....so I'll be peeved if building control have an issue. I don't 'need' it, its a stovax stockton 5, a 5kw stove, but i know a vent is good practice and a vent to directly by the stove, even if not connected to an OAK (outside air kit) means cold draughts across the room from some other leak/source of air are much less likely. so not only does the stove burn properly, the room is more comfy.
the 5kw cut off is a farce. that figure doesn't come from any tests and oddly enough its why lots of stoves that have a large firebox and can run at much higher power are rated to a nominal 5kw, as consumers like it, it avoid the part j necessity for a vent. a vent is good practice though. the sensible bit is the smoke chimney draw test....does it draw well? only trouble is alot of iffy installs could probably pass that test on a good day...a smoke pellet is perhaps not a great measure of draw but then its about the best practical test i guess.
my own house is probably a typical 1930s build, fairly leaky but changed over the years....originally with fireplaces in most rooms for coal fires, and air bricks in all rooms, but previous owners blocked up the fireplaces and put in central heating, then blocked up the draughty airbricks. then you get more damp/condensation. you install double glazing to cut down more draughts but get more condensation...you install bathroom and kitchen extractors to pull moisture out the house and prevent condensation. then i come along and want a stove....so i need to and have opened an air vent, added another vent in the back of the hearth from under the floor too. I do a chimney draw test and it passes but being belt and braces and having read part J i know to redo it with doors to extractor fans open and those fans running. i got it to pass that test too but not so easily...i had to warm the flue with a blow torch for 2 mins or else the kitchen extractor caused a reverse of flow and the smoke from the pellet came out the stove vent and filled the lounge. so although that test passes with a warm flue i'm also going to add another air vent in the kitchen wall to help the kitchen get its fresh air....I know from when i recently installed the kitchen that previous owners had blocked up 3 airbricks in the kitchen so putting one back is not going to be a bad thing....even though the kithcen doesn't have the range the house had when biult (so one should be enough i hope, not 3)
what i'm saying is, stoves need air and if you think it through carefully you can ensure they get it, in all circumstances, and in a way that doesn't cause cold draughts and comfort issues. I guess a good HETAS installer will know that...a good one.