What is the maximum altitude I'm allowed to fly a model plane or helicopter in England?
According to the UK CAA, a model aircraft is defined as:
any ‘Small Unmanned Aircraft (SUA)’ (0-20 kg) used for sporting and recreational purposes and a ‘large model aircraft’ is defined as any ‘Unmanned Aircraft’ (over 20 kg) used for sporting and recreational purposes.
The following rule applies to all "small unmanned aircraft", i.e. up to 20kg:
(3) The person in charge of a small unmanned aircraft must maintain direct, unaided visual contact with the aircraft sufficient to monitor its flight path in relation to other aircraft, persons, vehicles, vessels and structures for the purpose of avoiding collisions.
The following rule applies between 7kg and 20kg only:
The person in charge of a small unmanned aircraft which has a mass of more than 7 kg excluding its fuel but including any articles or equipment installed in or attached to the aircraft at the commencement of its flight, must not fly the aircraft:
(a) in Class A, C, D or E airspace unless the permission of the appropriate air traffic control unit has been obtained;
(b) within an aerodrome traffic zone during the notified hours of watch of the air traffic control unit (if any) at that aerodrome unless the permission of any such air traffic control unit has been obtained; or
(c) at a height of more than 400 feet above the surface unless it is flying in airspace described in sub-paragraph (a) or (b) and in accordance with the requirements for that airspace
So in theory, a model aircraft weighing less than 7kg could be flown to any altitude, with the only limitation being the requirement to keep in it sight. From 7kg to 20kg the altitude is 400ft, unless you meet the airspace requirements. In practical terms, the requirement to keep the aircraft in sight "unaided" is the main limitation and that restricts the altitude of smaller models in particular.
If it's over 20kg, the model aircraft is subject to all the regular UK aviation rules but in practice a written exemption is required:
Large model aircraft having a mass between 20 kg and 150 kg are subject to all of the Rules or Articles of the Air Navigation Order. As many of these Rules are practically impossible for the model operator to meet, the modeller must request a specific written Exemption to allow the model to be flown
The CAA homepage for model aircraft is here.