National Rail has been updated with the trains that will run. Source : https://www.nationalrail.co.uk/service-disruptions/industrial-action-july-20230625/

1. Depends on multiple factors but expect 45 min-1h from leaving the aircraft to the train station.

2. Check National Rail. The easiest route (fully included in the pass) is :

- Elizabeth Line Heathrow Airport - London Liverpool Street

- Greater Anglia London Liverpool Street - Cambridge

About 22nd July : seat reservations are optional in the UK but CrossCountry services are always packed. You'll surely have to stand. If you don't want that, buy a bus ticket (do not wait).

EDIT : If possible I'd take the bus on 22nd July. The journey is too complicated otherwise, going via London, etc.

- Megabus Cambridge - Birmingham 14:45 - 16:40 20£ per person

Do not wait to book. All coaches will be fully booked soon due to the strike.

For the 20th Elizabeth line Heathrow to London Liverpool Street and Greater Anglia Liverpool Street - Cambridge. The last train from Liverpool Street is listed as 21.28.

For the 22nd there are no direct Cambridge - Birmingham trains, with connections it would be possible but those trains are short to begin with and I would expect them to be very overcrowded..

Via London will likely be the better option, it looks as though there will be 2 trains an hour London Euston - Birmingham but expect these to be very busy.

For that, either use the route to Liverpool Street and take the Underground to Euston Square which is a 5 minute walk to Euston

or

If there is a train to Kings Cross take that, Kings Cross is a 15 minute walk to Euston.

At Euston there are 2 train companies,

London North Western are running 1 train an hour to Birmingham, this is a slow service with many intermediate stops.

Avanti West Coast are likely to be running 1 train an hour (Train to Liverpool via Birmingham) which will be faster. They haven’t finalised their timetable as yet.

If you decide to get the train from Cambridge to Birmingham on the 22nd (I think you’ll need to change twice), the longest leg is with Cross  Country. To reserve a seat on that train you could try emailing them: sales.support.crosscountry@trainsfares.co.uk

Booking a seat should normally also work online via GWR:

Thank you very much for all of your advice!

It seems that the traffic on 22 July will be quite unpredictable. We decided to take a bus from Cambridge to Birmingham in the evening on 21 July and have already bought the tickets.

We now hope that we could be able to catch a train to Cambridge after we landed on 20 July at 6pm. Otherwise, we will have to take a bus or call Uber which are both quite expensive options. 

“For the 20th Elizabeth line Heathrow to London Liverpool Street and Greater Anglia Liverpool Street - Cambridge. The last train from Liverpool Street is listed as 21.28.”

We tried to reserve seats of “Liverpool Street - Cambridge” via ACP but is not successful.

Please ignore ACP. They charge €6 for reservations in Great Britain that are free of charge elsewhere.

Online, you can book via GWR, see this post:

You can not reserve seats on trains on that route.

The operator claims (in their MERITS data) that you can.

Not the first time that is incorrect for British railways.

The only trains run by Greater Anglia that carry reservations or 1st class are their London - Norwich service.

I just did make reservation on the route from Liverpool Street to Cambridge. I have received a confirmation email which looks very formal.

One question is that I do not need to enter any names of travellers in the reservation. Is it normal?

That's normal. Traditionally, reservations and train tickets did not carry any name. For optional reservations, this is often still the case.