BLENHEIM & OXFORD

You can take the train from Paddington Station in London to Oxford which is an 1 1/2hr trip, there are five trains every hr. Then from Oxford train station take the S2 bus to Blenheim. Blenheim is only 8 miles from Oxford so you could take a taxi if you wanted. I would get to Oxford by 9am which get you to Blenheim around 9:30am giving you a lot of time at Blenheim. We were there most of the day. Do visit the butterfly house when you are there.

If you are interested in seeing Churchill's grave, it's at St. Martin's church in Bladon which is in walking distance from Blenheim.

Have a great time.

I was lucky when I went because we had a car. We did Bath in the morning, Blenheim in the afternoon and stopped in Oxford for dinner. It's definitely do-able in 1 day.

Blenheim is very easy as a day trip, anyone can do it.

In addition to the frequent train service from Paddington there is also the Oxford Tube bus ervice that starts at London Victoria and goes through/near the hotel districts at Marble Arch, Lancaster Gate and Bayswater too. This offers a 24 x 7 service with frequencies about every 15 minutes. Its much cheaper than the train (16 GBP return) and buses are nicely equpped double decker with washrooms, free wifi etc.
It also has the advantage that it terminates at the Central Bus Station in Oxford where you get the Blenheim local bus. The train station is a 5 minute walk only.
If you want to explore the grounds and do everything at Blenheim you will be there nearly all the day.

Oxford would be a great place to have dinner in the evening and walk around when the tour buses have gone before getting a late train or bus back to London.