If you hold a UK passport, you can enter Thailand on a 60 day non-exemption. Even if you go to Singapore and Vietnam within the 60 days, you will be fine entering Thailand again unless the Immigration Officer detects you are coming in and out of Thailand on 60 day exemptions and extensions too many times. There is no set number of times you can do this. I don’t think this applies to you so I won’t elaborate. You will need to complete a TDAC each and every time you enter Thailand. Google TDAC and its timelines for completion. You will need a visa to enter Vietnam. You can do this online. Singapore you can enter w/o a visa for stays up to 90 days. You need to complete a SG arrival card. Make sure your passport is valid for 6 months after arrival date.
right, it’s up to each individual to decide how to proceed. I’ve been coming to Thailand for 30 years on non-exemption, tourist visa, Non-B and now I am retired on non O-A. Like you, I never used and agency, always did everything the prescribed way and never once had an issue at any Thai border crossing. You are right, some dubious looking characters get admitted.