Transit in 2 airports in China, total transit over 24 hr, not going outside, transit Visa required?

Yes, unfortunately, you need a visa obtained in advance because your entire transit time is longer than 24 hours and you have more than one stop in China. This is valid for both UK and Nepali citizens. Saying that you are not leaving the airports is not valid because you will perform immigration formalities in Shanghai and your next flight will be a domestic one. In other words, you will formally enter China in full sense of that word.

I advise you to obtain Chinese transit (G) visas as soon as you can because they are the easiest to obtain since you have a proof that you will be really in a transit. I'm sorry for bringing you these not so convenient news, but obtaining the visas in your case is simply inevitable.

As a british passport holder, i am thinking to get 72 hrs free transit visa once i land in Shanghai Pudong airport rather than applying for transiti visa in london. Is that a bad idea?

Unfortunately, you are not allowed to do that because there is no 72 hour visa free transit in Shanghai, but 144 hour visa free transit and even if it were actual, you cannot have more than one stop in China even under 72 hour visa free transit. Having more than one stop is allowed only under 24 hour visa free transit, but your total transit time exceeds 24 hours. Consequently you will have to obtain a Chinese transit (G) visa in advance.