Is it possible to fly from UK to Hong Kong, onto Guangzhou then to Beijing and back to the UK?

If you describe your route right, HK- Mainland China - UK, it's a valid route for the 240h visa-free transit. Just remember the immediate stops before and after Chinese mainland should be two different countries/ territories (HK, Macau and Taiwan are eligible territories in this case). Stopovers count as immediate stops in this case and influence the 240-hour transit.

More things to note in your case is that you need to fly or take a ferry to go from HK to Guangzhou. The high speed train from West Kowloon Railway Station is not eligible. But within Chinese mainland, you can travel by any transport, including the train from Guanbgzhou to Beijing. Also, when pass the immigration in Guangzhou or even before you board the flight or ferry to Guangzhou, the flight ticket from Beijing to UK will be asked to present.