In order to use aDSL or cable internet, you must use a modem. The mode takes the analog signals that the ISP uses and converts them to a digital signal that the computer can use. Weather or not you want to use the modem the ISP provides is upt to you, but if you don't you'll have to check to make sure the modem you are going to use is compatable with their service.
The WRT45G is not a modem. It is called a broadband router because it is designed to share the internet service provided by the modem, which has only one ethernet port and normally only one IP address to hand out, to multiple devices. If you are planning on using more than one computer at a time with your internet service, you will want to connect the router to the modem, and then connect the computers to the router, either with a cable or wirelessly.
As far as what type of service to get, that depends on if you are looking for capacity (often referred to as speed) or affordability. I'm not familiar with the particulars of ISPs in England, but aDSL tends to be cheaper due to the reduced cost of infrastructure, whereas Cable usually provides the better throughput.
While prices and throughput will vary for both over time, the physics involved does not change. The theretical throughput limit of a transmission media is proportianal to the bandwith of the frequencies that propigate well through it. Coaxial cable, due to it's construction, allws a much greater range of frequencies to be transmitted with reduced interferance from outside sources, when compared to the twisted pair cable that is used in the traditional phone lines. For the forseeable future, any technology used to provide aDSL will yeild greater throughput if applied to cable instead.
So, if you're looking for "fast", go with the cable. If you're looking for cheap, go with whatever's cheaper in your area.
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