I want to move my internet connection to another room. The wire going into my modem is plenty long enough but when I had a fireplace fitted last year they put the wire behind it and I cant get it out

just before it goes behind the fireplace there is still enough wire to take the modem where I want to. My question is can I cut the wire Just before it goes behind the fireplace and reconnect the end onto the cut end or do I have to get telewest out to do this for me dont really want to pay out for what seems like a simple job.
Thanks
Debbie