From the LRA terms and conditions regarding recovery after an accident..
"If Your Car has a Breakdown as a result of a motor accident and You have comprehensive cover under Your motor insurance policy then, on request by You or
(in Your absence) the Authorised Driver and subject to the following conditions, We will arrange for Your Car to be transported from the scene of the Breakdown
to the nearest Lexus Centre or, alternatively, to another single destination in the United Kingdom chosen by Your motor insurers at their cost:"
https://d3rvezpmgp265q.cloudfront.net/lexusone/lexgbenv11/LRA-brochure_tcm-3157-1272758.pdf
Those three words in bold would mean one would need to get authorisation from the insurer that they would foot the bill. My guess is they would prefer to use their own nominated recovery service?