Now that the Covid rules are easing, my wife and I are considering plans to see my extended family in London and Birmingham.  I will probably spend a week in each city before returning to the United States.  Due to the kind of work we both do, we were thinking of traveling in September of next year like from September 6th-21st.  What will the weather be like during those weeks in both cities?  I know London has a lot of great things to do, but what would the best things to do in a week's span?  Also, how long is the train trip from Birmingham to London?  On our return trip, we will fly out of London Heathrow.  Generally speaking, how much times does it take to get through security and such from entering the airport to getting to the departure concourse.  Finally, what is the latest Covid Protocols for people entering the UK from America?

September is often nice and warm, in the 80s. But this is England, the weather can turn on you just like that

The train from London to B'Ham (pronounced Brum) should be about 90 minutes to two hours from London Euston Station IIRC, I haven't done that trip for many years (google will help here). As for intl travel and CV19 procedures I cannot help you there, not been out of the country for two years, they usually advise arrive 2 to 3 hours prior to departure but that was 'before'.

So much to do in London. Where to start? Museums (Imperial War Museum is good, many are free or a small donation), theatre, shopping, eating out, The Tower, Buckingham Palace. Some of the guided tours are surprisingly good even for a local, giving a lot of little bits of strange but quirky info on the city. It is one of the best cities in the World and has a very varied and sometimes shocking but always interesting history. Hidden London (hiddenlondon.com//) and (Secret London secretldn.com/) are good resources if you like the different sort of tour.

For B'Ham you'll need to ask a local. The only thing I know there is the Ming Moon restaurant, nice Asian/Oriental food buffet.

If you have family here they might be able to suggest more suitable options as they'll know your tastes and interests better. If they're a bit more extended than that, some idea on your likes etc might help.

James Purdey & Sons in london if you are into shotguns, birmingham gun quarter for gun history in Birmingham you might need to book in rather than just turn up.
If you travel a bit more north to staffordshire i would take you shooting
Atb

Thank you for your information.  It looks like we will have a good chance on having good weather.  We are really looking forward to our trip.  One more thing, what is the best way to get over jet lag when switching over the eight hour time zone change?

Jet lag is a bitch coming east. When we go to Az I have always found it easy as we naturally wake up in the early hours and get the day moving. By the time I've acclimatised and returned home I feel the need to lie in until midday.

I think it just needs you to get up in what feels like the middle of the night and go cold turkey. That's how I do it, I try not to sleep on the plane and stay up after I land until the normal (local) bedtime and force myself to adjust.