Here, just a stone's throw from the Houses of Parliament, you could almost be in a quiet monastery in the countryside and the serenity makes it a very relaxing space, even for godless souls like your author.
If you're not interested in paying the rather steep entrance fee for the rest of the Abbey, access to the Cloisters, and the College Garden which has been a site of continuous cultivation for more than 900 years, is via a small doorway in Dean’s Yard. From the courtyard at the front of the Abbey go through what looks like the gates to the Westminster School field, and then turn left and continue to corner of the yard (Dean's Yard) and go through the doorway. You should now be in the cloisters.
The cloisters are open from 8:00 am - 6:00 pm, but you can only enter for free after 4.30pm on weekdays and 2.30pm on weekends. At all other times you must enter via the main entrance. For more (limited) information visit the Westminster Abbey Website at http://www.westminster-abbey.org/visit-us/
Click here to see the location on a map, and an arrow which should hopefully clear up the rambling directions above.