Looking for advice on the following itinerary. I'm in the early stages of planning this trip. We are active couple in out late 30s who have travel some in Asia and Europe but never the UK. The only thing in stone are the dates to arrive and leave London. Stonehenge is a must and obvious first time London sights. I was also wondering if I should drop something and add the lake district but unsure about the weather and activities there in March. We do not plan to rent a car and want to use public transportation. Complete open to any changes at this point.
Thursday, March 1, 2018 Leave USA
Friday, March 2, 2018 Arrive London (Travel to Bath)
Saturday, March 3, 2018 Bath
Sunday, March 4, 2018 Tour Stonehenge
Monday, March 5, 2018 Travel to Cotswolds
Tuesday, March 6, 2018 Cotswolds
Wednesday, March 7, 2018 Travel to Stratford
Thursday, March 8, 2018 Currently Open unsure what to do with this day.
Friday, March 9, 2018 Travel to Liverpool
Saturday, March 10, 2018 Liverpool
Sunday, March 11, 2018 Travel to York
Monday, March 12, 2018 York
Tuesday, March 13, 2018 Travel to London
Wednesday, March 14, 2018 London
Thursday, March 15, 2018 London
Friday, March 16, 2018 London
Saturday, March 17, 2018 London
Sunday, March 18, 2018 Fly Home