BRP- middle names shown on passport but not BRP

[mustafamukhtar66]

Appreciate your help moderators.

I have a BRP which shows my name identically to my old passport which expired in 2015 (only first and last names), the authorities in my country -sudan- have changed the way names are appearing on passports; therefore has been issued with my full name (including the middle names) making it different to the BRP which doesn't have the middle names.
I just realised today that I should have notified HC through TOC. however I am due to apply for ILR in 2 months time. I knew the postal process of TOC might take time.

my question is; if I get a supporting letter from my country's embassy to justify the change and submitted that with my ILR premium application, will it work or am I being too naive.
any advice please??