Train to Norwich, Bury St. Edmunds?

Not sure what you call "dependable". Cambridge and Norwich are both at the far edge of commuter range, and get daily commuters as well as leisure and business travellers. Bury St Edmunds is closer to London.
Fast trains to Cambridge every 30 mins. From London Kings Cross, with slower trains from Liverpool Street.
Hourly (at least) trains from London Liverpool St to Norwich or Bury St. Edmunds.

Bury St Edmunds is in the Liverpool St to Cambridge route. You can also get direct trains between Cambridge and Norwich. So you can travel between these towns by train without doubling back to London.

You can look up times and buy tickets on the National Rail website: http://www.nationalrail.co.uk/

Both Norwich and Bury St Edmunds have old trains which are being replaced. There are problems with the overhead electricity from time to time and there are sometimes track problems, but the strikes are now no more because the company has seen sense and retained its guards for the benefit of the passengers.

So, reliable? Yeah, pretty much. Plenty of engineering work on weekends.

The trains to Cambridge from Kings Cross and St Pancras suffered from the over ambitious new timetable, and while still not God's gift to railway passengers it is much better than it was. The cardboard seats aren't great and if you are past average size they may be a bit small, but all these lines will move you effectively from A to B.

Do you know exactly which airfields you are tracking down? Most are now farmers' fields and may have a strip of runway left, most don't. Some few are used for flying.

There are resources available, and drone videos of some - often there is a veterans group or historical group. There are often plaques at or in local churches.

Having the car at Cambridge is a good idea. Be prepared for a longish drive to Norwich.

Maybe you would be interested in a swing by to visit this air museum.
Just south of Cambridge is the Imperial War Museum Duxford:
https://www.iwm.org.uk/visits/iwm-duxford
A part of this is The American Air Museum:
https://www.iwm.org.uk/events/american-air-museum
This is one of the largest air museums in Europe. This was an airfield during WW2, and some of the display areas are in WW2 hangars.
Just thought I'd mention it, since you'll be so close.
We enjoyed it very much.

Thank you each for your input. It is so helpful to have insight when embarking on this journey. One of the airfields was Attlebridge which was north of Norwich (& which is now the largest turkey farm in Europe) & the other was at Bury St. Edmunds.

Cambridge is a beautiful city but driving inside the city limits is not for the faint of heart - busy roads and lots of bicycles. From Cambridge, Bury St. Edmunds is an easy drive on the A14. From Bury to Norwich you will go through Thetford and onto Attleborough. I am not so familiar with the air bases in that direction, but there were many WW2 airbases a little further south that I am familiar with which are now just farm lands or industrial areas. https://www.abmc.gov/cemeteries-memorials/europe/cambridge-american-cemetery - may be a place of interest located near Cambridge. Another vote for Duxford Air museum. Are you just going to do this all in a day? or spending the night somewhere in the East Anglia area? it really is worth a day or two - Pretty villages and lots of history. Cambridge in itself will take a day to look around.

Duxford is great, but you could spend a whole day there and your schedule is already pushed to squeeze into one day.

The Shuttleworth Collection at Old Warden near Biggleswade, 25 miles west of Cambridge would also be of interest to you.

Oh gosh, I didn't realize you were going to cover all this in one day?!? Cambridge and Duxford and and and Norwich and Bury St Edmunds all in a day from London? Oh my.

Something will have to give, I'm afraid. I hear at least 3 or 4 days in there.

I took my family on a day trip from London to the Parham Airfield Museum, but we pretty much had enough time to train there, eat lunch, tour the museum, and train back. The most unreliable part was the London Metro (halfway there it was announced that our subway train wouldn't go all the way to the stop we needed for a reason I've now forgotten). And the local train stopped at a nearby town, so we needed a taxi from there. In hindsight renting a car in Cambridge or Ipswich would have been a good idea.

If you have extra days and like horses, the National Stud in Newmarket is very interesting.

Again, I thank you each for your insights. With our limited timeframe, we have now decided to forego the journey to Norwich & Bury St. Edmunds & will concentrate our day on the recommendations made for the Cambridge area. It sounds much more fruitful given our timeframe this trip.

On the food front on a trip to Cambridge, a couple of wee suggestions.

If you'd like a nice Tea in Cambridge you could do much worse than Harriets. https://harrietscafetearooms.co.uk/ They have locations in Bury St Edmunds and Norwich in addition to the superb one in Cambridge. https://harrietscafetearooms.co.uk/our-tearooms/cambridge-city-centre-tearooms/

A quick and easy standing up lunch can be had at one or more of the stalls at the open market - everything from Lebanese to Dim Sum and most ports between. On decent days there is also a Dim Sum cart, near the road, in addition to the Dim Sum bun place opposite the Subway. Cheap, tasty, and very local.

Then there is Fitzbillies. Sicky Chelsea buns. Say no more... http://www.fitzbillies.com/