Hi Dave,
Yes, you could pay 50K off reducing your mortgage to 106K and then having 50K in the offset, but you would need to check that you are allowed to make overpayments greater than 10% per year as this is usually restricted during a fixed term (or perhaps with a penalty). See below about having the money in the offset and having a mortgage (if it all went wrong).
Check out the FSCS site for more info on the protection, but my understanding is that if anything happened, the money that you owed the bank would be deducted before you are given compensation.
So the offset would be used to reduce your mortgage and you would receive no compensation, but in effect you would be no worse off.
In the case of having 100K in savings (or deposit as they call it) then you would only be compensated for the first 50K per name (joint names = 100K) per institution group, so potentially 50K worse off.
Not sure the UK banks are that much at risk, but that's what we all thought before!
http://www.fscs.org.uk/
Sparky.