I would say that this is highly dangerous. It is against US and Canadian code to not have outside ventilation for any fuel-burning appliance in your home; that's your furnace, HWH and stove/oven, assuming all are NG or propane. It is only acceptable to have a "filter-only" vent hood for your stove if it's all-electric (which BTW is the case for every single apartment I've ever rented; gas appliances may be cheaper on utility bills in the US, but a gas stove is a huge fire hazard and general liability for any landlord).
The code is in place for a very good reason; not only can inefficient burning of fossil fuels produce carbon monoxide and smoke (both of which continue to cause damage long after you've reached fresh air), but even when these fuels burn ideally, they remove oxygen from the air and replace it with CO2. CO2 in itself is not toxic in the same way CO and soot smoke are; as soon as you reach fresh air the symptoms of CO2 asphyxia begin to dissipate, while soot and CO poisoning ("smoke inhalation") can kill you hours after you reach fresh air. However, the consumption of oxygen and production of CO2 in a space with inadequate ventilation is a double-whammy for anyone in the same space; the oxygen is being consumed so there's less of it even in upper strata of the room's air, and as the CO2 builds it settles downward in a "blanket", pushing oxygen up towards the ceiling and away from you.
As the CO2 level builds, your body's natural "inhale/exhale" reflexes go haywire in a Catch-22 condition called hypercapnia; your natural breathing while in a high-CO2 atmosphere actually increases the CO2 levels in your blood, but the only thing your body can do to reduce CO2 levels is breathe. So, you start hyperventilating, which only exacerbates the problem. Should you pass out from lack of oxygen, you will not wake up if someone else doesn't get you out of the room or get some ventilation of fresh air through it.
Your landlord is running illegal housing. However, he may not know it, so be nice at first. Follow standard procedure for maintenance requests, and ask the landlord to install a proper outside vent line for this fume hood. If he refuses or drags his feet, you can call in the city's Code Compliance officials, or federal HUD (Housing and Urban Development) representative, and they will MAKE the landlord comply. Depending on the terms of your contract, the landlord may be giving you a free out by not living up to his end, meaning you may be able to break the lease at no cost if this has gone on for some time with the landlord's knowledge and inaction.
Understand that the cheapest way for your landlord to fix the problem with tenants still occupying the units may well be to cap off the gas feed and replace all the gas cooktops with the cheapest electric setups he can find. If this was the reason you moved in, and you don't get a "free out" from this debacle, you may find yourself stuck with a spiral-coil POS.
I realize that this is a U.S. reference, but you may be able to find a wall exhaust fan locally similar to this.
![Broan Motordor 360 CFM Wall Exhaust Fan](https://i.stack.imgur.com/QLkAJ.jpg)
You need to find a unit that is intended for exposure to the outdoors. Also you may need a cover in the colder months if the unit you find does not have a self closing louver. The one depicted does.
If you use 110 voltage and 60cycles, you may be able to order something like this from the U.S. Otherwise, be sure that it matches your local electric supply.
Best Answer
Are you sure these aren't part of your HVAC? If I had to guess, these are natural draft returns to the boiler room. If your heat comes through a grate in the floor, you need these.
Ok, you have radiators, so these probably are just fresh air intakes. Covering them or not is your prerogative.
Temporary solution: tape some card stock over the opening.
Semi-permanently: use a can of spray foam to totally fill the duct. You may need to get the grate open to stuff something in there, so the foam doesn't just drop down into the duct.
Permanently: remove the grates, and if necessary, remove or bash the remaining duct work into the wall with a hammer so that you can plaster over it, after having stuffed a piece of batt insulation into the duct.
Magnetic duct covers are another option.