I look at the number "44118501" and see that the last six digits could be a directory enquiries service; 118501. See Crosby Directory Enquiries.

I am a subscriber to PlanetTalk/Primus service. I am frequently getting billed on a no. I do not recognise. It apears on my itemised bill as   
  Directory Enquiries DQ 11    44118501
I have contacted them before but they insist I made the call. I would not use D.E. by phone only by i/net.
  In addition I thought all phone nos. in UK had to start with a zero?  Any thoughts please.

The number is 118501, the digits 44 being the international code for the UK.

There are numbers and access codes that start with 1. A few years back, six-digit directory enquiries numbers beginning with 118 were introduced.

I put 118501 into Google and the first link that came up was a thread on MoneySavingExpert.com started by someone who found entries for this on their bill.

Although the OP didn't bother to reply, suggestions were made that this could have come about due to mis-dialling of the 18185 prefix which is used by a call provider. Basically, if the second digit is missed out it becomes 1185. If one then goes on to dial a number with an STD code beginning 01, the number then dialled becomes 118501. So if the number started 01234567, then the number 118501234567 would actually connect to 118501.

Could this be a possibility here? Has someone in your household registered the number with 18185?