how to travel to england cheap?

you need to write a better question

try again please. What do you want to know? If you want to know inexpensive fares from your home it is unlikely that anybody other than you can guess where you want to travel from. If you don't say where in England you want to go it unlikely that anybody else can know.

We can guess but why bother?

It appears that the OP might be a non-native speaker posting here for the first time (an assumption, so forgive me if that is not the case). As a teacher of English as a second language, I’m thinking that perhaps he or she did not know how to phrase a question to get the best response on this site. Hochien, If you tell us where you are coming from and where in England you would like to go, I’m sure others on this site will be happy to help. You can also check a site like Google flights, where you can put in your cities and it will give you an idea of the cost. There are several people on this site who have been extremely helpful to me in my trips to England and I’m sure you will find the same once you provide more information. I hope that helps! 😀

I will try to assist, since we are very fond of traveling in the British Isles.

1. London is expensive, so travel to places outside of that city are more economical.
   
2. We have found much success staying in small hotels or Bed and Breakfasts. You usually get a very generous English Breakfast and can skip lunch (or just have a snack instead). Look on TripAdvisor for locations close to city center.
3. If you want to save more, you can purchase food at a grocery store occasionally. We didn't do this often, but on some busy days it worked.
4. Use public transportation or walk if you can. Taxis can be expensive.
5. If you plan to visit many historical sites, look a buying a year membership is something like English Heritage to save on visiting multiple sites. Must plan ahead.
6. For car rentals, check with Kayak and always have your own GPS (never rent from the car rental).

Personally I've not found London to be particularly expensive.

For accommodations check out YHA (Youth Hostel Association) at https://www.yha.org.uk . On my most recent trip to London I stayed at YHA's Saint Paul's location just a block from the cathedral in a single room for £35 a night.

So many museums and historic sites are free, those that are not free may offer a discounted entry if purchased online.

One thing I most often enjoyed was food/grocery shopping in the local shops and markets. It was the best way to enjoy foods that were uniquely British inexpensively.

English trains can be very, very expensive if you wait until the day you travel to buy the tickets. If you buy your tickets early, you may be able to get "Advance" tickets at a much lower price. Check on the NationalRail website. However, Advance tickets are not refundable and not changeable, so be certain you know your schedule before you buy.

If you are going to spend at least several days in London, you'll probably save a good bit of money with an Oyster Card, because each ride on the Underground will cost you less than with a single ticket.

Should I go to manchester? My favorite is Manchester City : ')

If you're already going halfway around the world, then do go to Manchester and tour the football grounds. We've found we have a lot of fun making the pilgrimage to places of pop culture and personal interest, whether it was the pre-condo conversion Battersea Power Station, Portmeiron in Wales, special museum exhibits.

Most UK grocery stores and supermarkets have good-sized takeaway sections (for sandwiches, pay a little more for the panini option instead of the squishy sandwich only a British schoolchild could love) and the museum/garden/national park cafes are often quite tasty and reasonably priced. Chain pubs will also offer 6-7 pound meal deals- sandwich, chips and small beer or soft drink.

You will generally find >https://uk.megabus.com to be the cheapest way of moving around from city to city.

For good value accommodation - if booked in advance >https://www.travelodge.co.uk
The previously mentioned YHA also offers value but be sure of what you are getting regarding shared dormitory v private room.

Purchase food in supermarkets.

For local buses :> www.traveline.info

It may be our method of travel, but we didn't find London to be overly expensive at all. Compared to what? People say New York City is expensive. We didn't find New York City to be expensive. People say Paris is expensive. We didn't find Paris to be expensive. Rome was supposed to be expensive.... not really. $120 to $ 145 a night, comfortable, clean room and with a private bath, "slightly," central location in any of these cities is what we paid and got all these nice services that went along with, included with, the room. Try and stay in down town Seattle for less than $120 a night. Wow!, now that's expensive.

As to our OP, I'm assuming this person to be using a translation app. Those work best if words and sentence building is simple. And who among us has not been, so far out of our language skills, that we didn't resort to Jargon and pointing, and some times made no freak-en sense at all to the locals?

Regarding how expensive is London, I would agree that compared to NYC, Seattle, Scandinavia, Switzerland, and Rome, London is not so bad.
Compared to staying in smaller cities and towns in Britain, London is more expensive. For example, in Chipping Campden, we had a wonderful spacious room with bath, in a perfect location for 80 GBP per night. We staying is some B&Bs for 60 GBP per night. We did pay more for popular places like Bath (about 100 GBP), but that included a wonderful breakfast.

i am asian, I intend to travel in the UK for 10 days, how much is the
minimum cost so everyone?

This is impossible to answer especially regarding the minimum cost starting with airfare. Are you flying from Dubai, Tel Aviv, Jakarta, Tokyo, Shanghai, Mumbai, Seoul, Ankara, etc?

Manchester is excellent and can be done inexpensively outside of match days. I know Man City offers stadium tours. There’s also the excellent., and free, National Football Museum in Manchester. There are plenty of other museums in Manchester as well. I particularly like the small and free Manchester Art Gallerty. You can find a budget hotel in Manchester under £50 outside of major events.