travel from Heathrow to Chipping Campden

Not "tube" it does not go direct to Paddington! Use Elizabeth Line, which is also run by TfL but not from the Underground stations at Heathrow, it uses the Heathrow Express platforms but is cheaper. And more importantly Elizabeth Line stops at Hayes &Harlington from where you can transfer to another of their trains to Reading and miss out Paddington altogether, then join the Paddington to Moreton-in Marsh. This can be bought as a through ticket Heathrow-MiM not via London and worthwhile savings justify the extra transfer.

Great! Thank you for this information!

First off, there is always the possibility of some type of strike action on the Tube,
so be alert to that.

From Blackfriars to/from Wembley, use the Transport for London trip planner to
find best route at the time you plan to go. While I would hazard a guess that
District or Circle from Blackfriars/connect to Jubilee to Wembley Park is the
most efficient Tube Route (and there are other options involving trains), on
the day you want to travel, there could be delays on any route, especially
at rush hour.

me.crewe has addressed the Chipping Campden part of your query...

I forgot the concert travel. Wembley Stadium has it's own station on the national rail route out of Marylebone station or is 15-20 minutes walk from Wembley Central on the line from Euston (also has tube trains if running). So if there was a problem with the tube then it's not a huge problem.

With tube, start at Blackfriars station (or walk the first part) to Embankment then take Bakerloo line to Wembley Central (or get out at Marylebone and use trains to Wembley Stadium). The Marylebone trains often run special timetables for big concerts.

Without tube, start at Blackfriars station (Thameslink section) to St Pancras, then walk 10 minutes to Euston for Wembley Central train or 205 bus to Marylebone.

If you were already out of the hotel in the afternoon you'd almost certainly be even closer to wherever you need to be to head to Wembley!

No idea what time the concert ends, the last trains into central London are at around midnight on normal dates.

I will answer your Wembley query- as someone very familiar with NW London, to travel between Blackfriars and Wembley Stadium, I would take the Thameslink from Blackfriars to West Hampstead, then change for the Jubilee line to Wembley Park. Note this change requires you to walk a block from the Thameslink station to the tube, but it's a very easy and quick change. When you exit at Wembley Park you'll be looking straight at the stadium and you can just walk right up to it. Then do the same in reverse. The Thameslink trains aren't as frequent as the tube but they are very frequent- like every 10-15 minutes.

You will find you are surrounded by other fans on the journey- we can always tell when something big is happening at Wembley based on the composition of people on the Jubilee line. I remember once the train driver even making an announcement to passengers that he'd ensure they were on time for their date with Harry Styles.

I'm not exactly clear on your plans. Are you staying at the Hyatt Regency Blackfriars when you fly in as well or only when coming back in for the concert? If not, where are you staying as that may change how you get to Paddington.

Yes, we're staying at Blackfriars first night and also when traveling in for concert. Thanks, everyone, for such great advice!

We used Chipping Campden as a base for six nights, stayed at the Volunteer Inn, that has a great pub and Indian Restaurant.
We visited Oxford, Blenheim Palace, Stratford Upon Avon and the Cotswolds.

We rented a car and it worked quite well. Not sure how you will manage touring from Chipping Campden, since the train doesn't go there.

Where did you rent the car? We don't want to rent at Heathrow day of arrival since we're spending the night and next day in Londo. Read somewhere that renting a car is Oxford is a possibility. Suggestions?

From the Hyatt the quickest way to Paddington for a train to the Cotswolds will I think be a Thameslink train north two stops from Blackfriars to Farringdon and then the Elizabeth Line to Paddington. Both are full size trains rather than tubes.

For car hire Heathrow is a bit of a faff as you have to get back to Heathrow and then take a shuttle to the car hire depots. But they do have the advantage of long opening hours. You can hire from Oxford but the drawback there is having to drive out of and back into Oxford which is definitely not car friendly. Not a great place to seat driving on the left if you're not used to it.

Alternatives for car hire are Didcot (has Enterprise car hire) and Swindon (Enterprise and Europcar). Both quick to get to from Paddington but a bit further to drive to Chipping Camden. Cheltenham is another option, near Chipping Camden but a bit further on the train. Bear in mind depots at these places are likely to be open 9-5 only and probably closed on Saturday afternoons and Sundays.