We would not consider this to be anti-social behaviour.
If you can hear your neighbour walking about and it is disturbing you, you should have a friendly chat with them, as they may not know that you can hear them.
If you feel you cannot talk to them, please use a Dear Neighbour card [pdf] 469KB.
If you feel that the noise is persistent enough (lasting longer than thirty minutes a day, more than five days a week), or at night time (after 11pm and before 7am), and loud enough, you can contact your local council and report the problem to the Environmental Health or Noise team.
Remember that no house or flat is totally soundproof - everyone can expect to hear some noise from neighbours.