Does anyone know what type of anaesthetic is used for having your tonsils removed and whether you need to stay in over night?

You do need to stay overnight and anesthetics would be general. As to which brand or how administered would depend on the anesthesiologist. He will assess you on age, weight, alergies, medical contidions.. etc. Here are some drug names.
Desflurane (Suprane®)
Droperidol (Inapsine®)
Enflurane (Ethrane®)
Etomidate (Amidate®)
Halothane
Isoflurane (Forane®)
Ketamine (Ketalar®)
Methohexital (Brevital®)
Methoxyflurane (Penthrane®)
Midazolam (Versed®)
Nitrous oxide
Propofol (Diprivan®)
Sevoflurane (Ultane®)
Thiopental (Pentothal®)