
Lu, hope your move went as smoothly as it possibly could and you're now settled into your new home
Most T'Interweb packages require a phone line for you to be able to connect and surf, which means line rental needs to be paid, even of you don't use the landline for calls. There are some packages which don't require a landline, but they often come with much slower speeds than a fixed line connection, and download allowances/limits tend to be much smaller. This isn't really problem if your usage isn't particularly heavy, with general surfing, email, FaceBook, Skype type activities, but if you want to do something more involved it can become rather laggy and slow.
Some mobile phone operators offer Have a look at the Linky for some examples, costs etc. If you have a mobile contract and your provider offers USB internet, there's always a chance that with a bit of cheekiness you could be able to negotiate a special deal

With USB internet the connection is always with you, wherever you may be, you just plug the dongle in and away you go. The downside tho is that, in some areas reception can be twitchy to say the least, usually due to areas having inadequate mobile coverage.
Another option might be a cable connection, like what Virgin provide, but this is only available in certain areas at the moment. Altho it tends to be lightening fast, it does come at a higher cost.
The only way you would be able to connect via someone else's connection, esp a secured one, is by them giving you the password to access it. I haven't been able to find anything about any packages for sharing between different locations. You'd have to track down who the connection belongs to, get to know them, then broach the subject of using their connection. The drawback would be you could only use the connection whilst it was active, if the account holder were to turn their modem off, then you'd be stuck until they powered it up again.
If you have a mobile phone package with a data allowance, you can attach your phone to your lappy via its USB cable and use it as a modem to access the web. Drawbacks to this tho are the speed of the connection, which can be extremely slow. Depending on usage, it can really eat into your Data Allowance, and if you were to exceed it, additional charges could be incured.