Many people who do not ordinarily use a mobile phone may wish, nonetheless, to have the use of one while cruising the canals and waterways. Overseas visitors may also find this desirable. What they need is a mobile phone for a relatively short period of time (as opposed to normal long term contracts).
The mobile phone can also be useful in connecting a laptop to the internet. High speed internet access via mobile phone ("broadband" or "3G" or "4G") is available in the UK, but can be spotty along the canals. The older, slower, internet access service is called "GPRS". But be sure any internet access plan you are considering allows "tethering" of the phone to your laptop.
Phones may be hired (rented) on a short term basis. However, I have dropped coverage of these plans as my impression is that it is much more economical to purchase a phone (prepay phones) than to hire a phone. A number of plans like this are listed below, but there are probably more. (Please let me know what you find, as I don't have the time to research this myself. This page is but a minor part of my whole web site.)
You will need a "GSM" phone. (Many mobile phones available in the United States are not GSM phones. Check with your carrier.) Unfortunately, even if you have a GSM phone, a US wireless provider will probably charge you $1-$2 per minute for calls in the UK/Europe. However, if you can get your US provider to "unlock" your GSM phone, then you can buy a "sim card" (about the size of a postage stamp) from a UK or European carrier, and be able to pay normal UK or European charges for calls. These are usually called "sim-only" plans.
If you do not have an unlocked GSM phone, you will need to buy a GSM phone. Because of the unlocking problem, foreign visitors should wait and buy the phone from their carrier of choice after their arrival. Shops are easily found.
Note that with pay-as-you-go plans, you load your sim card with money that you spend-down in calling. Sim cards are easily refilled - petrol stations and large supermarkets usually provide this service.
Not a phone hire firm, but the Boater's Phone Company web site provides useful advice about phone selection for boating use, for both voice and internet.
As for everything on this web site, I have no relationship with these companies. This material is for information only.
Note: The "best/least dear" way to connect to the internet, from a boat via a mobile phone, is constantly changing. For the latest suggestions, post a question on the canals mailing list.