We have a block of 4 IP addresses x.y.z.116 to x.y.z.119

Our bank keep disconnecting us and say that the IP Address they monitor is continually changing.

If we use a site such as http://whatismyipaddress.com/ it shows that the last octet is continually changing with values in the above range.

Our ISP (Plusnet) say that the IP Address is rock solid (x.y.z.117) and suggests there is an issue with our router (Vigor 2820).

I changed the router to a Vigor 2600 and the problem is still there allbeit that the change of address appears to be slower.

Any ideas please

It sounds like Load Balancing is working. This usually causes https web access to respond as you describe. Hence, the typical solution is to have a load balance rule to shove all https requests out though one particular wan/ip.

I suspect you may have got this fixed already but in addition to nealuk's suggestion, if you've got multiple WAN IPs set up using WAN IP Alias, make sure to untick "Join NAT IP Pool" for those additional WAN IPs as that'll cause the same problem.