I'm not sure, but check the terms of your lease - are the people upstairs allowed wooden floors (if they have them)? Wooden floors are terrible for transferring noise and often aren't allowed in flats.
Are you in a period building or a new build? I think regulations were introduced a few years ago for new developments and if they are not adequate you might be able to get it checked out under the terms of your NHBC cover if it's a new build.
Judging from the situation you describe, I'd infer that you're likely to be living in a period building, where this kind of issue is quite common.
It is more effective, by and large, for the soundproofing to go in the cavity under your neighbours' floor than for you to create an extra barrier in your home by fitting a layer of sound-deadening material. However, the latter is obviously easier to do, because it's typically very difficult to persuade an upstairs neighbour to let you conduct building work in their home.
In terms of creating an extra layer of insulation in your own home, you'll need to have the ceiling lowered and you can then fill the artifical cavity with a material such as Rockwool. This can be quite effective, but is an expensive thing to do, and you will obviously lose some ceiling height, which may be undesirable.
No one has answered the basic question though: Is it effective? I was planning on doing this some time ago being in a flat with tastefully varnished floors and for the sake of my neighbours.
Alas, I couldn't justify the cost without knowing the effects so ended up just putting a heavy carpet down,bit of a shame really. I imagine proofing helps but if your neighbour spends their time walking around their flat in stilletoes probably still problematic.
Filling the space between the floor is the most effective option as it acts as a sound resonator (think of an acoustic guitar).
The reason the question can't be answered readily is that soundproofing's effectiveness is (a) to some degree a matter of perception, because different people have different acoustic sensitivies and (b) variable according to other acoustic factors.