A lookup of telco allocations reveals:
0845 121 and 0845 123 are allocated to Affiniti Integrated Solutions, a part of Kingston Communications. The change date is 11/1995 for both. 0800 915 is also Affiniti, date 10/1997
Within the London code (020) there are quite few Affiniti prefixes:
020 1173 02/2005
020 1174 03/2002
020 1222 02/2005
020 1227 05/2007
020 1228 05/2007
020 3130 06/2005
020 3131 06/2005
020 7160 07/2003
020 7788 05/1999
020 8181 06/2001
020 8185 02/2005
020 8712 02/2005
As you can see, there's loads. The first five are "national dialling only", meaning that you have to dial 020 code even when calling from a landline with an 020 number. It is also not possible to call some/many of these numbers from BT landlines. They are usually used where the number isn't publicised such as routing 08xx/09xx numbers to. That in no way means that the alternative to the 0845s we are seeking are contained within these prefixes. Indeed, I found the number for Pets at Home helpline to be 020 81819000. This is the same as the 0800 for them.
In short, consider the length of time that these numbers have been in service and the fact the old ones have now been reused. In which case, I think 020 8181 is worth a try. Remember, it's all ifs and buts though.
A check of Crawley (01293) reveals only one Affiniti prefix: 01293 83, change date 03/2004
I believe that it's a needle in a haystack you're looking for.