If one is not happy with the performance of the franchisee (Lexus Dealer), then it,(not Lexus UK) is the first port of call.
Request in writing a copy of the franchisee`s Complaints Procedure, (email is an excellent way) and complete the procedure to the spirit and the letter.
If at the conclusion of proceedings, you are still unhappy and if the matter has stopped short of involving the Dealer Principal, write to him/her stating clearly and unequivocally why you remain dissatisfied. If after receiving his/her response, you remain unhappy, then involve Lexus UK stating your reasons for remaining dissatisfied and provide copies of all correspondence to date. Do not do anything that would amount to you as the complainant not following procedures.And stick to the facts.
By all means ask for advice on this Forum,but do NOT name names.