There are many flavors of "wireless", and your choice depends on what you want it to do for you.
The most common type of wireless is 802.11 (which comes in many sub-types, B and G being the most popular for computers). These allow near LAN speeds, at relatively short range (10-100 meters, depending on your setup). There are "hot-spots" at bookstores, cafes, etc. that provide access for a fee (sometimes monthly, sometimes purchased as needed, often included with purchase of some product).
Another type of wireless access is GPRS, which is derived from the GSM system used by cell phones. There are multiple kinds of GPRS access, with speeds ranging from 20000 bits per second (bps), to 2000000 bps and beyond. The range for GRPS runs from 2 kilometers (km), to over 10 km, and depending on your carrier often blankets an entire metro area reasonably well.
There are a number of wireless laptops available for under £800, you shouldn't have any problem finding several that suit your needs and offer some choices. Without knowing a great deal more about what you want, I couldn't begin to offer suggestions in that area.
Assuming that you mean 802.11 (any flavor), you'll need to get it for both your laptop and your broadband connection. 802.11 is typically supplied as part of the laptop, or it can be easily added via a PCMCIA card. It may or may not be included in a broadband connection such as a DSL or cable modem.