Unless I'm missing something there isn't a geographical no for DL Motor Claims on the list against 0845 246 1110.  Some sweetie managed to write my car off and I'm doing a lot of contact with DL.  Sorry if I've missed it - I'm new to all this

It's commonplace for companies to have different 084x/087x numbers for the same purpose. They can gather statistics so may advertise different numbers in different places.

A search for direct line reveals a number of results. Some unverifieds are picked up because they have "direct line" somewhere in the entry eg "Direct line to John Smith".

All Direct Line switchboards are listed, and they will put you through. Alternatively, in this case a customer services operator may be able to put you through to claims.

Direct Line used to use 01/02 numbers. Across its offices the last four digits were, I believe, the same (note how the switchboards all end 3313). I have an old letter for Direct Line motor insurance and at the top are two numbers for the Leeds office, both of which now give a recording redirecting to an 0845 number.

The numbers are:
Customer hotline: 0113 2809922 (Message redirects to 0845 2468811)
Claims: 0113 2456860 (Message redirects to 0845 2468471)

There is a Bristol customer services in our database which is 0117 9849922. Note the last four digits are the same. If you change them to the last four on the above claims number you get claims. I tried it and it was answered within about 5 or 10 seconds. The number is 0117 9846860. 

Doing this for other offices:
Croydon:
020 86869922 Message redirects to 0845 2468811
020 86866860 Message redirects to 0845 2468471

Manchester:
0161 8399922 Message redirects to 0845 2468811
0161 8396860 Message redirects to 0845 2468471

Birmingham:
0121 2369922 Message redirects to 0845 2468811
0121 2366860 Answers as "Direct Line Motor Claims" and says that the call is held in a queue

Two other numbers for claims are 0113 2927339 and 0113 2927100.