If you intend to be in Thailand long term then you’ll want medical insurance and travel insurance.
Travel insurance generally only covers for x number of days, but works well for flight delays or lost baggage and such.
Medical insurance is probably way cheaper to buy in Thailand. Check out policies from AIA, AXA, Luma, Allianz etc. buy direct from the company rather than a brokerage site that claims to offer the cheapest deals for expats.
Point of being pedantic but you don’t hold an English passport. You may well have a British passport, and if you do you can travel to Thailand and enter visa exempt with a stamp for 60 days.