Buy UK Train Tickets Online

This site will direct you to the relevant train company where you can buy tickets

http://www.nationalrail.co.uk/

For London to Durham the train operator is https://www.virgintrainseastcoast.com/

The cheapest tickets are called Advance, which as their name implies must be bought in advance - you must travel on the pre-booked train.

Alternatively, it might make sense to get a connecting flight to Newcastle and take a train from there to Durham (you can just buy a walk-up ticket for that short journey).

If you are heading for Durham right after landing, allow sufficient time for flight delays, long passport control lines etc. It is often recommended to allow a 3 to 4 hour buffer between scheduled arrival time and onward travel that involves prepaid inflexible tickets.

For train tickets, go to the Virgin Trains East Coast website. You can get the Piccadilly Line Tube direct from Heathrow to King's Cross station, and then the VTEC train from there.

If you're flying on British Airways or American from Philly, perhaps you can add a connecting flight to Newcastle? It's a shorter journey from there to Durham and just as easy (Metro from Airport to Central Station, train from there to Durham)

Although ignorant about apps, I know first-hand that trailine is an easy and useful way to book trains at scant extra expense. That's particularly true of its continental Europe branch. Everything is open to criticism on the Internet but almost all mentions of trailine I have seen are positive.
Anyhow, if you can find a direct flight to Manchester or Newcastle it will save you some hassles getting through big-city London. Reducing stress following a trans-Atlantic flight is a worthy goal.

You may well have a special reason for wanting to go to Canterbury. If not and you just wish to see another British city -why not visit York as it is on the rail routes between Manchester Airport / London (Kings Cross) & Durham
http://www.visityork.org/?AskRedirect=true

If you are going to do a lot of rail travel in Britain, you may be eligible for a Railcard - which will cost £30 for a year but give you about a third off. https://www.16-25railcard.co.uk/using-your-railcard/are-you-eligible/

This is a short video that may be of interest:>https://www.youtube.com/watch?v=fVoWSTHcnmo

Never understood Trainline's popularity myself. As far as I'm aware it's sort of a rail amalgamator, in that it takes away all the hassle of operating companies and routes and whatnot and just says 'here, put in where you want to go and when, and we'll do the rest'. If I'm correct, it does the exact same thing that the National Rail website does, except tacks an extra fee on top for the effort.

"Nationalrail etc is very confusing, in my experience. "

Not mine. You do have to learn about the rules for each kind of ticket (e.g., not all tickets bought in advance are Advance tickets), but that's true no matter where you buy the tickets from.

Both the National Rail app and the National Rail website worked fine for me.

Trainline is still popular because it was about the first on the scene and formally owned by Virgin and Stagecoach amongst others. The only competitor back in the day was Qjump, which Trainline acquired. Now owned by Kohlberg Kravis Roberts.

I hope Charlotte is better at running a B&B than giving out travel advice.

eh?

Nigel, I was confused too. I assume Charlotte deleted her post.

Definitely leave plenty of time for delays or cancellations. We just returned from a trip in the U.K. that literally saw multiple train delays/cancellations. We missed a train connection because someone pulled the emergency stop and the train got delayed for a decent time while they figured it out. The next day we were stuck on a rail as a rail bridge was struck by truck ahead of us and we had to wait while engineering ensured safety of the bridge. The following day saw Paddington station closed for the entire day for a fire followed by a later delay as someone was fatally struck by a train. Basically my point is, if traveling by rail, ensure that you leave some leeway. On a bright note, none of our trip was hindered by these delays, only lost sleep.

If you take the train out to Canterbury, you leave from London Victoria train station, choose to arrive at Canterbury East. The city center and cathedral is a 10 minute walk from the train station.

It sounds like the recommendations to fly into Manchester are most helpful.