Problem buying rail ticket London to Oxford

Try any other TOC (Train Operating Company) website: GWR, LNER, for example.

This has been reported before on another forum, on South West Trains from memory. Trying from the UK the reason for the problem could not be replicated.
That user succeeded using the LNER website.- https://www.lner.co.uk/
It is not clear why man in Seat 61 suggests Transport for Wales.

I just spent another 30 minutes trying to book on GWR (that is the company that operaates the Oxford train, BTW). All went fine until I got to the payment page. After entering all fields the Buy Now button lit up. When I hit it, the page refreshed, all my info was there, but the transaction would not complete. It can't be that there's anything wrong with my card because it said the card info is entered on the next page, which it won't advance to.

Really frustrating!! Is there a phone number I can call?

It's surprisingly hard to find a phone number- they want you to do it electronically, but I've found one- 03457000125
(you'll need to convert that into an international number from the US, I don't know how to do that). They are open from 0600 to 2300 GMT- it is now 10.49pm.
I don't know why payment is not working- it's OK this side of the pond.
This is how they prefer contact, again 0600-2300 GMT- https://www.gwr.com/help-and-support/contact-us

I always start at the National Rail site.

https://ojp.nationalrail.co.uk/personal/home/search

It will take you to the GWR site for the purchase. Of course I could not enter my credit card to see if it would go through, or fail at the final step, so cannot duplicate your problem. But were you looked in to your GWR account? Is it possible your bank is blocking the transaction?

It could well be a card-security issue; those aren't exactly rare.

However, it's always worth trying the transaction with a different browser. If the problem persists, try a different device (smartphone, tablet, PC). I've twice had problems buying US tickets on the TicketMaster website that were solved by switching devices.

First, try calling your credit card company to see if the payment is getting through to them. They will be able to tell you if there have been any attempts and make sure they are not rejecting the charge. I have had situations where my card company blocked the charge and they needed to do something before I could retry.

You are outside of UK business hours (assuming you’ve just done this). You may want to try again tomorrow when it is between 9 and 5 in the UK. There is always the possibility some kind of system maintenance is occurring.

If you are unable to buy tickets from GWR, you can try buying from the trainline as a last resort. They charge a small mark up. I’ve been able to buy tickets on the GWR website in the past with my US card, but some of the other European websites have caused me problems and when they’ve failed, I’ve ended up using the trainline.
https://www.thetrainline.com/

The GWR app did have some general problems yesterday but it does have the hallmarks of a 3d secure issue. I'd try LNER.

GWR website says that t doesn’t work well outside of the UK.

I bought two sets of tickets on the GWR site yesterday. Encountered a similar problem when I tried to pay. I think it was my US address, not my AMEX. I had a saved address on the GWR site that belonged to friends who moved back from London several years ago. (I had tickets mailed to their address when I had a problem last time.) When I let the site use their address, no problem! Bought both sets of tickets using it. I had my tickets downloaded to the GWR app. The address I used has no relation to my home or credit card address.

I'm no authority on the British rail system, but maybe you could try putting in a London address - your hotel's, your apartment's, Kate and William's - and see if that works.

I tried again this morning, same problems. Went to a third party site, willing to pay a booking fee to get this done. The one I used was Trainpal, which I found through the National Rail site.

It was very easy, the exact same trains I had been trying to book through TFW and GWR, and the price was the same, no convenience or booking fees, and they emailed me the tickets, I didn't have to to DL an app to get them as was req by GWR.

Often UK websites do not accept North American Credit cards. This. has been reported as a problem with us trying to get UK SIM cards online. It is why I go directly to the shop. Trains are another matter, and I see the advantage in trying to book ahead, due to the sometimes exorbitant cost differences in waiting til you are there. I do not know what can be done about it, but I highly doubt your credit card company/bank is the issue.

I don't know what anyone needs an address for now to get train tickets. I'm never asked for that now, and haven't been since before Covid. All I ever need is my e-mail address and to check out as a guest.
I didn't think anyone still had tickets mailed out to them- I either have them e-mailed to me as PDF's or just get a collection code for collection of physical tickets from any station machine anywhere in the UK from 15 minutes after purchase to time of departure.
But of course I don't do things like apps. Sometimes the old school way works the best.
The LNER website has been proven to work with North American travel cards, which was proposed to the OP yesterday. As far as I am aware so does the Northern Rail website.

The LNER app allows download into Apple / Google wallet which these days I personally find more convenient than using the app at the barrier or messing around with pdfs, or downloading to my smart card. Some tickets such as any involving cross-London travel have to be still issued on paper though.