No-one will allow a mobile to access a contract-ISP account (0800 or 0808), so 0844/0845 is the only way to go as PAYG at 5p/min off-peak and not included in mobile inclusive minutes. I also have lots of unused inclusive minutes each month, but still have to pay 5p/min for internet access.
If you can find an ISP who will give you a geographic number, you can then use included airtime (free minutes).
When I was using a Vodafone mobile to connect, I used Easynet, who were happy to provide a London (0207) number, and it worked fine (and free) for several years.
I assume this technique still works - I stopped using it a couple of years ago.
Sooty