I have some boards at the fab shop for what I call my Weather Board, it will report air pressure, temperature and rel humidity on I2C. The overall size of the board is just over a square inch.
Keeping the price of the board down I made some choices of the sensors that may or may not meet your "very accurate" threshold. The accuracy thresholds may be a problem for relative humidity as the main need for the board was to measure the density altitude and humidity is least significant of the 3 measurements. You might want to tell us what "very accurate" means so then myself and others know if what have is good enough to help you out.
Being I2C for all the sensors it can easily be used with an Arduino and implemented with GPRS shield.