Fault on long SWA to Garden Office

What is going wrong is not having a professional install it and TEST it, before and after it is energised, according to electrical regulations. If you had done the above you wouldn't have had a problem.

you will either have a neutral to earth fault on the fixed wiring after the garage consumer unit or in the 16mm 3 core or one of the appliances you have plugged in is faulty if you have an RCD installed in both the garage unit and the house the one in the house needs to be greater than 30 ma as if they remain the same the fault will for want of better words take out the one with the weaker trip rate this can be tested to see if this is the case but testing the rcd alone will not fix the issue

This is one of those problems where testing by a tradesman would save you time and money. A simple thing to check is the colours used for the earth and neutral are they the same both ends, I recently had a similar fault to investigate where an electrician had used the wrong colours one end and someone else connected the correct colours the other end. Colours should be brown = live / black (marked with G/Y tape) = earth / grey (marked with blue tape)= neutral, hope this helps.