My cordless phone base in the office is adjacent to the office WiFi router.
My cordless phone base in the house is adjacent to the WiFi repeater.
If your phone and Wifi and interfering with each other you could try setting the router to a different channel.
It's not at all clear from your post whether your old phone was cordless or not.
It's also not very clear whether you have a combined modem/router or separate modem. You say that the phone socket is in the hall, but the router is in the living room, so I'm assuming that you have separates. If not, then it's not clear where, in relation to the router, the filter is.
There are two types of filter: those with a line socket and two other sockets, one for phone the other for modem/router, and those with just line and phone sockets. The former are really just combined splitters and phone filters. As Maydup says, it is only the phone (and every phone) that needs a filter. The modem/router should be connected direct, or through the correct side of a combined splitter/filter.