I lived in England for 20 years. March is going to be wet and chilly. Having said that, it’s a good time to visit in terms of seeing tourist sites. Bring proper rain jackets and appropriate footwear.
Around London:
Get the guide book, Hidden London. Full of cool little tidbits of info. Check things off as you see them. Fun.
If you plan to visit the Harry Potter Warner Brother’s studio tour, you might find my review helpful: https://www.tripadvisor.com/ShowUserReviews-g2691242-d2147749-r305532757-Warner_Bros_Studio_Tour_London_The_Making_of_Harry_Potter-Leavesden_Hertfordshi.html
Have tea one afternoon in London. You can spend a FORTUNE, or a lot less. If you want posh, got to Fortnum and Mason. I love, love, love that store, and I think it’s a million times better than Harrod’s. You can get the most amazing picnic/gift baskets there, in all price ranges. Buy handmade marshmallows in exotic flavors. They are delectable. My kids ask my husband to bring some home every time he goes to the UK for work.
I HIGHLY recommend you visit Churchill’s War Rooms. That’s my new favorite attraction in London. Within 2 hours of London, the best places to visit, IMO, are Bath, Cambridge, Hampton Court Palace, Hever Castle, Warwick Castle, Battle, and Brighton (and the Brighton Pavilion.)
Cornwall and Devon are gorgeous, but at that time of year, I’m not sure it’s worth visiting. You could do the hike to Land’s End though, which will go along the coast and should be very beautiful.
If you are including regions north of, well, the South and Southwest, Edinburgh is wonderful. You could go to the Highlands, which will probably feel wonderfully desolate. I love the area around the Yorkshire Dales and Durham. The Lake District is absolutely beautiful with lots of great hiking, but in March, I don’t know if it’s a must do. But there is so much to see that you might just have to brave it. I also love the Peak District. I love Chester, and the Cathedral there is amazing. The high street is filled with shops tucked away in genuine Tudor buildings.
Whatever you do, be sure to get out of London and see the countryside. There is something very special about driving around the winding country lanes, shielded by hedgerows on both sides, and wondering if another car is coming around the bend. Find some country pubs with a fire and have a Ploughman’s Lunch. Wander into a tea room and get a Bakewell Tart or a Flapjack, and a cuppa. Have a wonderful trip!