If I'm understanding you correctly, you could:
Sign up with a "free" ISP (like Tiscali) where you just pay for the phone call. Then you use pretty much any phone socket to connect at dial-up speeds. (Requires a modem).
Set up a home wireless network. You can then take your lappy into the garden. (Requires a wireless router, and for your lappy to have a wireless card - you should be able to buy one if not).
Get a 3G card or similar for your lappy. This enables you to use a cellphone network to get on the internet. I'm not sure what the costs are (not cheap, I suspect).
Use wireless hotspots in hotels/airports/internet caf�s/service stations/coffee shops. Not sure how widespread they are. (Assumes you have a wireless card in your laptop).