Thatcher, like many surnames is occupational in origin... but of course that was her married name .. her maiden name was Roberts..another main group of surnames being derived from Christian names ie Roberts contraction of Robertson.... (others having origin in appearance or location... my own more or less means troglodyte!) Name origins are one of my hobbies so I am more confident than on rooves......
There has been a small revival but it is quite a skill which takes time so learn
.... so good thatchers are few and far between...Thatching is quite a good trade if you can get an apprenticeship
thatch
But if you want thatch ...may I give a plug for my own
locale (once a Tourist Information Officer always a TIO!).. Swan Green is the classic postcard unsurprisingly.. and there is the most gorgeous one on the way to Ringwood.... I am afraid for me that the muralled one doesn't compare ...