mdf:

 

If you're using a telephone extension cable, I'm guessing you've got a jackpoint with a BT jack (flat, with the catch on the side) and using an ADSL filter with an RJ11 (catch on top, much narrower than normal/RJ45 ethernet jacks) cable between the filter and the modem/router. So it's BT --> extension --> filter --> RJ11-RJ11.

 

If that's the case, I think you want something like this: https://www.amazon.co.uk/d/ms5/Metre-RJ11-Speed-BroadBand-Cable-Using-Twisted/B008IKVCJW. Basically a long RJ11-RJ11 cable using higher quality ethernet cable with twisted pairs (8 wires, distributed into 4 pairs, with each pair twisted together to reduce interference. Though you only actually need one pair). Put the filter straight into the jackpoint, then run the RJ11 cable from the filter to the modem/router. 

 

And I guess that if the cost to have a master filter installed + the jack point relocated is outside my mother in laws budget, I could always go with the cable that you linked to. Obviously not ideal, but from what I understand, it's the next best solution.

I've got friends in the UK anyway, who I could have the cable posted to.