Stop over permit in airport of Beijing

Hi,

Can I get a stop over permit in Beijing China because we are going to have a 23 hour stop over there and would like to book a hotel outside the airport so that it will be cheaper. Is that possible for Philippine passport holder? I have a flight bound for Manchester and I was not able to get a transit visa here in the philippines because it was a rushed flight and China embassy here takes 2 -3 days rush for processing the transit visa. My flight is on tuesday already. What is the best option for me so our stay in Beijing for the stopover will be comfortable and low cost? Please help me on this. Thank you