Canterbury Cathedral

Not sure I fully understand your question, but if you have been to a service there, an additional 2 and a half hours should be comfortable time to continue touring the church (more interesing if you can hook onto a tour of the church- dont know if they do this on a Sunday). Canterbury itself has some interesting areas in the vicinity of the cathedral similar to York's "shambles' (mediaeval streets), a canal cruise and a ducking stool. You could easily spend two and a half hours in the vicinity of the cathedral. Once we took a train from London and spent a very full day just in and around the cathedral before training back that evening. I strongly recommend canterbury as a day trip from London

Not sure why you MUST see Canterbury Cathedral. From an architectural perspective there are loads of other Norman Cathedrals though not identical are just as impressive, if not more so. Westminster Abbey, St Paul's in London. St George's Chapel, Salisbury Cathedral and Winchester Cathedral to the west of London in my view are more impressive archtecturally than Canterbury and could conceivably be visited in one day or mix and matched with other worthwhile places like Stonehenge, Oxford and Bath in the same vicinity. From an historical perspective, introduction of christianity To UK, Thomas Beckett and all that, there is not so much to see as experience but this takes no time at all.
If you really are into history as much as that you really need to do Canterbury 'properly' and neighbouring St Augsitines and all the other places in the close, the Cathedral is just one building within the close. Visting on a Sunday is not a great idea as opening hours are so narrow, sqeezed in among the church services. It primarily a church first, tourist attraction last, so knowledgable guides and volunteers are more tied with church matters than tourists on a Sunday.

We have visited at least 9 English cathedrals and many abbeys--Canterbury was interesting, but not our favourite. We went for the Beckett associations, spent an hour in the cathedral, had lunch, then walked around a bit trying without much luck to make connections with Chaucer..... Since we had a car, we also visited Battle Abbey and Bodiam Castle that day. Both of those were more interesting IMHO......You might instead consider heading west, combining Winchester Cathedral and Salisbury Cathedral in one day. They make an interesting compare and contrast pair......But since this is your trip, only you can decide what you MUST see.

Since you'll be in the area, I'd encourage you to visit Canterbury and its cathedral. The town is interesting and the Cathedral beautifully set in it. You can park just outside the walls and walk through the old narrow streets, then through a gate and the Cathedral rises in front of you. Attending a service would be a bonus, I think, for the music and the atmosphere, a great way to experience the nave. I agree that two hours, before or after a service, should be plenty to see the cloister, the apse, the crossing (be sure to look UP), and the crypt. I found the Becket shrine moving, the various royal tombs interesting, and the stained glass beautiful. You don't really need a guided tour, though the one we took (on a weekday) was quite good. There are certainly other great cathedrals in England, but Canterbury is hard to beat for its historic importance, urban surroundings, and proximity to London.