The rule is 180 days per year in Thailand, it doesn't change anything if they are consecutive or not, it is cumulative. However, the UK signed a DTA with Thailand to avoid double taxation, i suggest you take a look on it.
i think you make a mistake with the rule that IO can ask to see 20.000 in cash in order to let a visitor into the country. (to prove they can support themselves) It is not a "fee".
based on which ground this fee is supposed to be paid ? It is clearly written at the airport to not give any money to IO's. This story seems fishy to me.