can we - Brtish passpot holders, apply for visa to China while in Singapore?

You can't apply for a China visa in Singapore because you are a temporary visitor to Singapore. Non-Singapore citizens shall provide documents that entitle them to reside for an extended period of time in the Singapore, such as a PR, WP, EP, STP, DP. Temporary visitors to Singapore should apply for a Chinese visa in their own country. For the special case, the visa officer has the rights to make the final decision on whether issuing a visa or not.