There may be some resources for you.
UKAS should be able to make available their ISO/IEC 17025 checklist, which you can use as a base for questions to re-write your QM. They also have a very understandable primer (well, as understandable as anyone's) on measurement uncertainty (MU) and you will need to become familiar with MU.
Identify the standards you actually use for testing. As an example, here in the U.S. we typically use ASTM (American Society for Testing and Materials) standards for various tests.
Get with the folks who actually do the given tasks, whether testing or purchasing or whatever. Have them describe what they do step by step. Then you have the base for the re-write, and it will reflect what you actually do.
I like the use of flowcharts personally as they are easy to use.....and after all, the folks need to use the procedures. Remember the KISS (Keep It Short and Simple) rule, otherwise the procedures will likely get ignored.
Setting up the manual so your paragraph numbers coincide to the Standard's number system makes it easy for your assessor and MAY reduce some nit-picky kinds of things.
Once you have all that, go through your system yourself.....try to access client information from a terminal that should not have access.....makes sure equipment is calibrated by an accredited calibration lab.....make sure any sub-contracted labs are accredited.....make sure the management review includes the mandatory topics in Section 4.14, and others beyond that are OK to have so long as the required ones are there.....if proficiency testing or inter-laboratory comparisons (PT/ILC) exists make sure you have them or are enrolled for them, and contact UKAS if you are not sure if any exist for your scope.
These are just a few of the basics, but should get you on the right track.
Let us all know how things go.
Hershal