Mobile broadband.
It's not as fast or reliable as using a landline but you can carry you "phone line" in your pocket. I use Vodafone at £15 per month for 24 months including the "dongle" (= the phone line!). It's marketed for people with laptops on trains but I use it to connect several PCs at several addresses to the internet (as long as I remember to take the dongle with me). If you are planning to use it at one particular address, check the coverage maps and order it via the internet so that you are covered by the distance selling regulations and you can cancel within a few days if the coverage isn't right at your address. (at one address, I have to use a 1m USB cable to dangle the dongle near the window to get a decent connection - I'm sure the neighbours don't mind :) ).
All the mobile providers offer mobile broadband but Three have a bad reputation for poor coverage. You can pay as you go for one month at a time on 30 day rolling contracts but then you've got to pay for the dongle.
Most older properties will have a phone line somewhere but it will cost to get it reconnected plus perhaps £10 (?) per month line rental before you even start talking about broadband.