Do future electrical works invalidate a satisfactory EICR?
The EICR is a report of the electrical installation at a particular point in time (like a vehicle MOT test certificate). It is not invalidated by any subsequent work.

Any electrical work done should be accompanied by a Minor Works Certificate (MWC) for small jobs, and this Certificate will be limited to the work done and will not test the rest of the installation. 

It is a requirement of the IET Wiring Regulations that work is tested and certificated, and a requirement of NICEIC membership to follow the IET Regulations and issue certificates accordingly. 

For rental purposes you would need an invoice to claim the cost of the work against tax, and a MWC to demonstrate compliance with your landlord's duty of care in respect of electrical safety.