Modifications to the vehicle which would render the information held by the DVLA inaccurate must be notified to the DVLA, usually with an engineers report, so they can update their records. This is not to say they are not allowed, simply that your 'log book' must contain accurate information about the vehicle. Such infomation includes - colour, body style, engine capacity, engine numbers, type of fuel used, number of seats.
Other modifications such as body kits, engine tuning parts, exhausts, wheels and so on are legal as long as the car is still roadworthy, for example wheels which make the tyre tread stick out beyond the wheelarch would fail an MoT, as would an exhaust which is too loud or windows that are tinted too darkly. Obviously the insurance companies would need to be informed but will rarely refuse to cover such modifications.