London: probably 25 miles for £1.50 (https://www.timeout.com/london/blog/how-far-can-you-go-with-...) or one of the rare £1 EasyBus tickets from Paddington to Luton which would cover around 37 miles.
The second one is not really public transportation though, and we're getting dangerously close to the £15 Ryanair flights territory.