Well you are going to miss something for sure. And does your England mean just that or does it include Wales, Scotland and Ireland.
In England of course there is London...maybe take the bus for the city sights to get the feel of the city. Depends then what your interests are. On my first visit I went to Hyde Park and The Barbican and the museums. Then took the tube out of town to Hamstead Heath.
You can do day trips from London...maybe The Cotswolds Great places and fun names "Burton on the Water" etc
Are you on tour with a group or on your own.?
I love the Lake District too. Lancashire and Cornwall is beautiful.
For me train travel is a favourite and BEFORE leaving Australia I buy a train pass. Then I can catch any train any time.
On my first trip to Scotland (on my own) I hopped on a train in Blackpool, changed in Preston and then on a train to Scotland which divided in half and I just went with my half.
As for France well most folk head for Paris and Montmatre and the like. All well known and famous.Plenty of day trips available. But there is also Normandy with the little towns of Bayeux and Honfleur.
There are some excellent VT members with heaps of info on France who will no doubt reply.
But perhaps a little more from you would help. Where are you planning already? What are your interests.
In both countries there are out of the way places and something different if that is your interest.

Well the eiffel tower and the big ben is a must, off course. You should see the buckingham palace, and the monalisa too. But some places like the vineyard in the southern france is a great place to have a picnic, and some small cafe have a delicious chocolate cake