There were in excess of 1000 teaching vacancies in TES last week.
You do not have to live in the most expensive part of the country. As an "essential worker" Mr Wench would qualify for assistance in buying a property (Shared Ownership schemes exist for that very reason). Anyway what is so great about owning a house? The upkeep alone will ensure you never have any money (am I not right Nick?) ~ at least when renting you don't have that to worry about. The problem is a lack of "public" housing, be it Housing Associations or Local Councils and for that we have to blame the British Middle Class obsession with property ownership. No other country has this problem and citizens of most countries are happy to rent. My niece (a teacher of infants) in Switzerland rents a suberb flat (three beds, dining room, living room, kitchen, shower room, bathroom and a cellar) from her local town council. Everyone does. Her neighbour is a doctor at the local hospital.
I have know Dutch people who rent their flat in Amsterdam and their weekend house in the country. They do not wish to own property.