You can see if a name is in use here
http://www.demon.net/external/
note ... your quoted url isn't a domain ... it's just a hosted site within the NTL domain.
as such it's part of your account ... as long as you have service the site is yours
from the domain naming point - note names are leased ... not bought
if it's free ... you can have it - but make sure it's yours BEFORE to publicise or (worse) print letterheads.
and note down the renewal date .... it won't be the first time a sniper has bought a successful domain name from under the nose of a late payment.