Don’t forget that you don’t have to continue say LHR-AMS on the same day as you arrive at LHR. I recently did BRU-LHR-DXB/HKG-LHR-BRU but travelled BRU-LHR one week before the LHR-DXB sector. On the return just under a week after arriving back to LHR. You can I understand stop over for a month.
There well may be an increase in airport taxes, but it will be a drop in the ocean compared to what you will be saving.