Assuming you mean a regular 30 day extension for a tourist visa or visa exemption, Bangkok usually doesn't ask, but some immigration offices may want it. I think it's best to have one just in case and as someone mentioned before it is a legal requirement.
I believe you have a UK passport, so when you arrive in Thailand you will get a 45 day visa exemption which is extendable one time should you decide to stay longer. Being that this is your first time traveling to Thailand, the odds of them asking for 20,000 baht is almost zero.
If I were in your situation I would try to get a tourist visa and have all the necessary documents and cash ready to show when arriving in Thailand. However, that still doesn't guarantee Thailand will let you in, it really depends on the individual you're dealing with. Hope everything works out for you.