https://www.crosscountrytrains.co.uk/travel-information/disruption/industrial-action

This was last weekend: https://www.bbc.co.uk/news/articles/c5y04nyjz29o

I can't find out what future strikes are planned, but it doesn't seem like there's been any progress to a resolution. You'd have to see if the services you want to use are run by Cross Country - quite likely, especially moving between Gloucester and Leicester (the other train franchises in England are mainly based as each radiating out from a London terminus).

...is that some of their services such as Reading to Newcastle do not have enough carriages and are hopelessly overcrowded in standard class as a consequence.

Fortunately I've been able to blag upgrades to 1st Class for my recent journeys to and from Oxford, which made a difference.

A few days in London. Then take the train to Leicester. A few days there then train to Gloucester for a few days. Then take the train to Oxford where we'll spend a few days. Then to Heathrow. I think there's a train or bus from Oxford to Heathrow.

Cross Country have a Leicester to Birmingham route, and a Birmingham to Gloucester, and I think without Cross Country, you might have to go all the way into London to do it. London to Leicester will be the franchise out of St. Pancras, I think, and Gloucester to Oxford can be done on Great Western with a change at Didcot Parkway, a little south of Oxford.

For Oxford to Heathrow, a bus is probably easiest - the train would probably involve changes, and a bus might even be direct with no stops.

To go from Leicester to Gloucester.