Couple of things - you've said 'pebbles' in the body of your question, not gravel, which suggests the stones are much bigger than gravel. Grass will not readily grow over the area because there's nothing to root into even if it is gravel; if its pebbles, it'll also be impossible to cut, being lumpy. Artificial turf won't work either if they are actually cobbles or pebbles. Second, does the area get any sun, or is it very shady? If its shady, then grass will do very poorly, even if you were allowed to remove the pebbles. If you were able to grow grass, do you have room to store a mower and edging shears anyway?
If it isn't shady, another option is to remove the pebbles, lay some lawn and do a bit of planting, in the sure and certain knowledge that you will need to restore the area to its previous condition before you leave. If you can't store the pebbles anywhere, that means you'd need to buy new ones, just the same as the existing, and have them laid - if there's a membrane beneath, you will need to replace that as well.
In the UK, 'small' means very small indeed usually - if the area is, say, 3 metres squared or less, having a lawn just isn't practical if you want to grow some plants, so you could forgo the lawn and remove pebbles where you want to plant in the soil, again knowing you will have to remove the plants and replace the pebbles later on when you leave.
If you intend to carry out either of these suggestions, it would be wise to run it past your landlady first, maybe sign an agreement saying you will restore the garden post your occupancy. If she still doesn't agree, then you can't change the area at all, and you will have to resort to potted plants only, arranged on top of the stones. Whether its shady or sunny is something that needs to be taken into consideration when choosing plants too.