OP - If you are starting with a new employer, why not spend the time with people at the new employer to learn the culture. What may have been the case in Asia in the past is not likely to be the case in the UK. Your employer may only care that the price of a Y ticket is GBP X and that is what the employer will reimburse, e.g., "lowest logical fare."

Conversely, in many organizations, people who hide simple things are perceived to be hiding things which do matter. That is a major negative and may be for no good reason.

Me? If there is no time before your first trip, suffer in Y. Figure it out and going forward, stick to the policy and the culture of the employer. Example. Many employers are just as happy to have you book and pay for J, so long as you properly document the cost of Y and only submit for reimbursement the cost of Y). That is sensible and reflects the reality of transparent business practice. It saves change fees and saves time.