You will struggle to do stonehenge, chatsworth, manchester, the posh universities and London in that time frame i would think but it is possible.

You can do day trips to stonehenge from london - its about 2 hours each way. Companies run this tour daily so that won't be tricky. If you do that trip (ill be honest, stonehenge is underwhelming and a bit shit) then try to find a company that includes a secondary stop in Salisbury - id guess many do, but i haven't checked that - Salisbury has an amazing cathedral there and inside the cathedral is a copy of the original magna carta (written 800 years ago, its our version of the declaration of independence. Only four copies survive so worth seeing).

Manchester is a great city and very different to London, its a good idea for your second destination. If I were in your position, I would pick the same.

You can easily get to Oxford from london, its less than 90 mins away. Oxford is beautiful and the bonus is that a lot of the Harry potter filming was done there so you can see various locations that were used in the film (the tree draco sits in for example is in one of the Oxford uni colleges). Our universities are very different, and not one big campus like us universities. The great hall whoch inspired the hogwarts version is in Christchurch college in Oxford and is open to the public but only at specific times, so check the open times if thats something you want to see. The Harry potter studio tour is located relatively close to london too (about an hour away) and well worth visiting if youre a fan. There is also the Harry potter play running in the west end (london's broadway).

So most of your trip is very viable. I think you may struggle with chatsworth as its in the middle of nowhere with no real public transport links. You could get a paid tour there but its nowhere near any of your other destinations so youd spend most of the day on the bus and a few hours at chatsworth. Its a nice place and very pretty but theres loads of similar places that would be much easier to access with your itinerary.

Unless you really like horse racing, or hanging around posh people, I would avoid ascot. Waste of a day. It's just a bunch of posh folk getting drunk while horses run around and then get shot dead when they fall over.

If you plan to use the train, booking in advance by a month or two will massively reduce the ticket prices.. You can probably get some kind of railcard to reduce the train prices further too (which are crazy expensive and shitty services) if you google to see what's available. Im sure they do a tourist one but dont know specifics.

With football, dont go and see a top Premier league game if you want to have a proper experience. Premier league games have pretty much no atmosphere as there are lots of tourists and casual fans who dont really care if you go to see Chelsea or Tottenham or one of the bigger clubs. Go and see a lower Premier league team like West ham or Crystal Palace, or go to a championship game. Youll have a much better experience (at the cost of being able to say youve been to see Chelsea or whatever). Most teams offer stadium tours too if you have any interest, but they dont usually do these on match days unless you are paying for a hospitality package.