Change of employment under Work Permit Scheme

[coe]

Dear all,
I have a quick question regarding "change of employment" for you:
I am in the UK on a work permit. I have accepted a job offer a month ago and my new employer has just arranged a new work permit for me. I haven't yet been through FLR-IED process.

However, in the meantime, my current employer is planning to offer me a new position which may make me stay rather than go to the new employer.

Once I am granted a new work permit, does this mean that I lose my current work permit, and lose my rights to work in my current employer? Is it possible for me to stay in my current job?
Your response will be much appreciated...
Thanks