I am a British guy, here to practice Chinese while solving your problem. For the UK, you should start your trip in London. I've seen London mentioned a lot in this answer. Well, I don't have to explain. But I also want to remind you that the cost of living in London is a bit more expensive than other places. This is an international city, there will be a lot of tourists, do not arrange too full tour, or you will be tired.
You might have a few options when you get to London. Here's a don 't-miss attraction. I think it was a big mistake to miss the northwest. The north-west was the economic heart of Britain decades ago. Manchester had more money than London. So the cultural and historical background is worth knowing. Besides, the scenery here is very English and the food is good too! To see the real Britain, go to the north-west. "Brother, how?" - I heard you say you can get there by train from any English city.
1) The Lake District
Just in the northwest of England, take the train to Windermere, a small town.
The Lake District is really the most beautiful part of England. The landscape has attracted all kinds of artists and poets. Like Beatrice Potter and William Wordsworth. Once you get to the Lake District, you start to love it. The old buildings, the English countryside, the unique mountains, the highest mountains and the longest lakes in England, the culture is still very rich. That all sounds great but the thing that really touched me about the Lake district is how warm the people are.
Take a cruise on Lake Windermere if the weather is good, or explore the local forests and mountains. On a rainy day (preferably between March and July), the Beatrix Potter's World gallery is a great place to get into the world of cute Peter Rabbit and fairy tales. There are also plenty of afternoon tea options in the Lake District, but the Beatrice Potter World Pavilion offers a different kind of high tea from a luxury hotel. They get all the cookies and sandwiches ready that day. The taste is super authentic, as pure as if eaten at home in the UK.
The Lake District is also the centre of Britain's great outdoors, so try something new here. There is "scrambling", for example. It's like climbing a mountain, except you go up a river, yes, in the river, not by the river. It's a little cold, but it's great fun, and the kids will love it. It doesn't matter if it's not for you, make the trip easy and give yourself time to walk around the lake.
Culturally, the Lake District has everything. England's most famous poet, Wordsworth, lived here and wrote his most famous poems. Head to Grasmere to find his old farmhouse, Dove Cottage. The landscape of the lake area is also influenced by human beings, but this is not a bad thing, just as the rice layer in China is more beautiful to some slopes, and the sheep in the lake area are more beautiful to the mountains in the lake area. I will quickly explain that in the mountains and lakes the weather is more severe in winter, sometimes it snows, sometimes it's windy and so on, sometimes it floods (don't worry, the floods here are not floods, it's still beautiful to visit the lakes in winter and there are fewer tourists). There is a sheep called Herdwick in the Lake District. The sheep can survive the winter on top of the mountain, so they are popular with local sheep herders and their meat is delicious. Now you'll only find purebred Herdwick sheep in the Lake District. Big or small, they're always cute. You see that most of the lake's hilltops are not covered by trees, and you know that now because this is where the sheep are raised. (Although it's a farm, the highest part is also open to the public, and you can hike along the trail - it doesn't matter if the sheep are there or not)