I plan to visit Shanghai on 144 hours transit visa

Your route is UK - SH - Delhi, right? If yes, you are eligible for the 144 hours visa free policy.
The prices accommodation in the city are a wide range. You can easily find one based on your standard. And the prices of high speed train tickets are also reasonable.

You don't need to inform anybody. You will just tell at check-in in UK that you will travel to India via Shanghai using 144 hour visa free transit.

Upon arrival in Shanghai, you will approach 144 hour visa free transit counter where you will fill out the blue form and after that you will get a sticker in your passport and be allowed to exit the airport.

This entire process and a sticker are absolutely free of charge.

By the way, this is not a "144 hours transit visa", but 144 hour visa free transit. There is no visa at all!