I am landing at LHR on June 12, 2022 at 9:55 pm. I only have 2 full days before I fly home on June 15, 2022. We can not change our plans due to work. We are going on a cruise and fly into LHR at the end of the cruise. Can I see all 3 of the above by public transport in 2 days? I would love to have more time but that’s not an option this time. Also where should I base for the 3 nights that would be easier and faster to get to these 3 places? The base can be London or some where else. Thanks for the help in advance. We just booked the trip today because we canceled our Baltic cruise due to the war.
Looks like Windsor Castle is closed on Monday and Tuesday per the website.
Blenheim Palace is in lovely Woodstock, a wonderful town to visit.
If Windsor Castle doesn’t work, consider Hampton Court Palace. Easy to get to and very enjoyable.
If you don't want to be packing and unpacking for two days, you may want to base yourself in an airport hotel at LHR. That's probably what I would do.
According to Rome2Rio, Blenheim Palace is 2 hours 17 minutes by train from LHR. Depending how many are in your party and how much you want to spend, you could make the trip in under an hour if you hire a town car.
Using Rome2Rio for Warwick Castle can be confusing because apparently there is a location in greater London by that name. Assuming you mean the actual castle in Warwickshire, from LHR it's about 2 1/2 hours by train and about 1 1/2 hours by town car. Note that it's operated by a private theme park company, so a more Disney-like experience than most historic castles.
So you could do those two in two days and have a reasonable amount of "on the ground" time to enjoy each. If they are open on Mondays and Tuesdays ...
Another comment recommended Hampton Court Palace as an alternative, but I see their opening days in June are Wednesday through Sunday. https://www.hrp.org.uk/hampton-court-palace/visit/opening-and-closing-times/
Checking the website, there are no tickets available for Windsor Castle on the days you have available.
I would suggest you base yourself in Oxford - travel there the first day and get settled into your hotel and spend the rest of the day exploring Oxford.
Catch a bus to Blenheim - details on their website. The palace and grounds will fill the day.
https://www.blenheimpalace.com/visitus/getting-here/
Next day catch the train to Warwick (about 90minute journey and plenty of trains). Visit the castle. St Mary's Church is also worth visiting and has the tombs from Warwick Castle.
Look at the geography and determine how you travel from each location, when they are open and how you could pull it off.
I have been to all three and don't see how you could do it.
Blenheim would be the place where you would likely spend the less time. If you stayed in Oxford, you might be able to arrive at Blenheim at opening, then head up to Warwick Castle. Still, we spent an entire day at Warwick Castle, I suspect you need a minimum of three hours there.
Windsor Castle is closer to London and could be done on a day trip from London. You will spend about half a day there, but there is time getting there and departing.