Alex James, all visas from the Thai Embassy, London require an ONLINE application before you send any documents. Consulates cannot do anything by post, you have to go in person.If you want a 3 month Non O Visa, then the required documents have to be sent by the consulate for approval to London, this is done electronically but can take 1-2 days for approval.
If you had been travelling after a stay in a hotel (who would have filed a TM30) then you would have nothing to show anyone ! The only reason they looked at your TM30 was because it WAS there. I am currently of the opinion that if you have no need to interact with immigration, visa or not, then I'll take my chance and not bother.
You can stay 30 days without getting a visa, however, the day you arrive counts as day 1. Airlines can be fussy if your return date is not within those 30 days.