I accidentally in your base

Tomorrow my modem/router arrives for my new ADSL ISP (Be). I've given my 30 days notice with my current crappy cable ISP (Virgin Media). Obviously I will be immediately switching my home LAN onto the ADSL router, but it occurs to me that I could also leave the old cable modem connected up and just take the password etc off of the wireless on that network. I won't be using it, but someone else might find it useful, and I'm still paying for the service until the end of the month so it may as well get used.

The only potential drawback I can think of is that if someone does something stupendously illegal using my connection, it's going to take quite a lot of talking to persuade the relevant authorities that it wasn't me that did it...