I don't have an OML, but I'm fairly sure you are correct in that you can train with one. The CAA will be able to tell you for sure, but that doesn't stop schools from making their own rules. It might be worth seeing if you can speak with the CFI or someone senior within each school and ask them to confirm. It would be wise to back this up in writing.
Failing that, Stapleford, ACS Flight Training and Euro Flight Training are some examples of modular schools with a good reputation.