What documents do I need for visa exemption entry to Thailand from the UK and how can I extend my stay for another 30 days?

On your Arrival, you will need to show your passport...(you may be asked where you will be staying ... Just have the address of your first few days in Thailand).

If you have a recent history of living in Thailand during COVID-19, then be prepared to answer the question WHY do you visit again?

Otherwise, no problems.

Enjoy your holidays in Thailand.

AND if you don't have a return ticket departing Thailand, ask your airline if they will ALLOW you to fly to Thailand.

And the OP has said to me that he does have a one way ticket to Phnom Penh Cambodia to show if asked on check-in for his Flight from the UK.

Nothing required. For extension you'll need to pop to the local immigration office wherever you're staying. It's a same-day thing usually, might need to pick up next day. Go a couple of days early. The application for extra 30 days requires passport picture and copies of passport (all pages)..