JM, applying for a UK service record only requires printing and filling out a couple of simple forms and sending off the payment and a copy of a death certificate.
I would imagine it would be a lot more trouble and be more time consuming to request the RSL or an MP to intervene in any way. I'm not sure if they would have any knowledge of the process (particularly the MP) or if they would be bothered to get involved - they'd probably just point you in the direction of the UK gov website if they are aware of it's existence.

The 'problem' is what is the easiest, and most cost effective, $ to £ payment method.
