DHCP and DNS may be the issue
I had a neighbour with this problem last weekend.
They had been sent a replacement router from BT but still had problems.
I changed their Windows 10 PC to use google's DNS servers and everything started working again.
All my windows PC's use fixed DNS servers and I've not run into this problem so far.
I've not had any real issues with my HH4 and FTTC. The only real issue I have with the HH4 is the complete lack of being able to configure them to my liking, such as pointing at a set of DNS servers that are not BTs. Any suggestions?