reserve specific train from Oxford to London?

On any other operator than HEX the cheaper advance fares are on one specified train.

Miss that train and it's a new ticket.

Here on Northern, in truth no-one ever cares or checks that you are on the booked train. I have no idea of whether Great Western are any more rigorous in checking.

So it may be better to just buy at full price at the station, and accept the cost, if you don't want to be hanging round

Advance tickets are for specific trains, not all day. If you can work out when you will finish lunch and get to the station you can get an Advance ticket for a Sunday in October for £6 per person.

Walk up tickets, Sunday is off peak all day, Off Peak Single are £31.70 per person.

Which is more important to you, money or planning?

GWR will pick up travelling on the wrong train with an Advance if there is a ticket inspection.

Sundays can be surprisingly busy and so you may find a reservation useful even with tickets that aren't tied to that specific service.

How are you getting to Oxford?

Marco, we have a rental for 2 weeks as we travel around the Lakes and Yorkshire. We will return the car in Oxford late afternoon, then take a walking tour of Oxford the following morning before training into London.

To all of you, thanks for your responses.

have you double checked the Saturday hours of the rental place?

Yes, good question. I have checked, and the Oxford train station office is closed when we will return the car. It's not ideal, but we've done this before and are OK with the arrangement. We will take time-stamped pictures of the car before we leave the station. We've never had an issue, but we will be ready if there is a problem.

Instead of the train, you can take the Oxford Tube (www.oxfordtube.com), which is a bus that runs 24/7 between Oxford and Victoria Station; it makes a handful of stops in central London.

Here’s a review of the Oxford Tube in the London-Oxford direction from YouTuber whom I particularly enjoy: https://www.youtube.com/watch?v=_0wV_M1CSrM

I'd just choose a time after 2:30 and reserve now for a great price. I just did the GWR from Oxford to London last Saturday and it was on time and not crowded at all. It was a very speedy trip and I would not hesitate to do it again. It was quite cheap booking far enough out so I sprung for first class for our family of 3. It was a very quiet car seated around a table, but nothing special - no drink cart or conductor.

One more thing to note - traffic and road closure construction at the station means you need to be prepared for heavy traffic in central Oxford. Check Google maps, etc but I experienced this last Saturday and Tuesday. We rented with Hertz on Osney Mead, which is a 14 min walk (.7) miles from the station. On pickup, I did not notice a road closure because the pedestrian route is open. On return from the Cotswolds, my ideal plan was to drop my family and bags at the station, drive 4 mins to Hertz, then walk to the station to meet them. There is a major road closure right at the station and due to the geography, the drive from the station to Hertz is a 6.5 mile detour of 20+ minutes. This surprise nearly made us miss the train.

Thanks for all the advice. Recap: I bought our tickets yesterday on the GWR site for the 3:56 pm departure from Oxford to Paddington. Our hotel is a short taxi ride from Paddington. I got the low advance fare and chose the 3:56 departure so we will have enough time for lunch and a wander before we head for our train. It's never made sense to add stress to what is supposed to be a relaxing trip. Besides which, we don't have a deadline for arrival at our hotel, so what's the hurry! Just dinner and a sleep :)