If the address is Vicarage Gate, you require St Mary Abbots Church Hall, and not the church itself. (They're a quarter of a mile apart)
The Transport for London journey planner suggests taking the Piccadilly Line to Gloucester Road and then the Circle Line to High Street Kensington. As Dzug states, you should expect a journey time of around an hour.
From High Street Kensington station, turn right onto Kensington High Street. After 200 yards, bear left (by St Mary Abbots Church) onto Kensington Church Street. 300 yards along, Kensington Church Street curves off to the left but you should continue walking in a straight line, into Vicarage Gate. A short way along, you'll see a turning off to your right (which is still part of Vicarage Gate). The church hall is at the end of this turning.
As Dzug states, the fare is �4 each way. If you're going to morning exams, a Day Travelcard won't help you (because you'd have to pay the peak-time fare of �13.20). However, if you're travelling to an afternoon exam (so that your journey from Uxbridge will commence after 0930), you can buy a 6-zone off-peak Day Travelcard for �6.70.
Also as Dzug states, there are further minor savings to be made by purchasing an Oyster card.
Chris