There are three channels at customs:
Even if you come through a 'Nothing to Declare' channel, the customs personnel still have the right to ask you to open your luggage. NEVER agree to carry anyone else's luggage through customs.
You should seek advice from the British Embassy or High Commission in your home country as to what you can and cannot bring into the UK.
Personal belongings are normally permitted as long as they are for your own use and will be taken home at the end of your stay in the UK.