A who.is check shows the 22.214.171.124 IP address originates in Lithuania. A Google search of the IP address also found it on a SIP attack (a type of flood attack against internet VoIP phones and clients) IP block list.
Have you tried the following?
Power down the Belkin router (I'm assuming this uses standard unmodified firmware) for 5 to 10 minutes to close all connections and increase the chance of being assigned a new IP address. In this time also disconnect all computers / systems from the router.
Power up the router and allow it to connect to Plusnet. Allow the router to run for about 5 min before choosing one of the computers to connect to the router and to the internet. Check the router logs and see if there is any suspicious behavior and if there is did it occur before or after the computer was connected to the router.
If there is no suspicious behavior in the log then disconnect the computer you just used and try connecting another computer to the router. Hopefully this will allow you to find which computer is requesting / starting the suspicious traffic. From your description in the original post I suspect that the router is crashing periodically due to excessive traffic. The DROP IN=ppp0 error means that you have been disconnected from the Plusnet gateway hence no internet connectivity which will then mean that Windows will not be able to resolve DNS requests leading to the DNS errors.
A very useful program for monitoring outgoing internet connections from Windows systems can be found here:
You will need to run it in administrator mode (right click on icon and select "run as administrator").
As for your Plusnet IP address not originating in the UK I believe this is because of Plusnet have purchased blocks of IP addresses from other ISP's and then have been slow updating the country location with the various IP databases. This can lead to problems when trying to use a UK credit card as a fraud alert can be generated (many internet credit card transactions will check the location of the card against the location of the IP address and expect them to match). I believe there have been messages about this in the Plusnet forums in the past but I am not sure if this is still an on going issue.
Hope this helps.