Having recently revamped my network this is a subject I am more familiar with than I ever wanted to be. From your description it sounds as if Modem B may not have a working connection to your phone line. Try some simple troubleshooting and perform the following tests IN ORDER.
  1. Double check the wire connecting Router B to the telco wall jack and be sure both ends are completely and firmly inserted at both ends.
  2. If the wire connecting Router B to the Telco wall jack came in the box with Router B? Try switching to the connecting wire you used with Router A.
  3. If you are using the wire that come with Router A, try switching to the connecting wire that cam in the box with Router B.
  4. If Router B still won't connect, verify you have good connection to the telco by checking to see if Router A still works.
  5. If you have preformed each of the checks and Router B still does not connect the failure would appear to be either an electro-mechanical or configuration problem in Router B. — Since Router configuration is different from brand to brand and even model to model within a brand we would have to know the make and model number of your Router to go much further in troubleshooting. Hopefully there would be someone here who is familiar with the particular Router and any eccentricities.
MY SOLUTION:

I had a similar situation with coverage that I had attempted to solve with a new expensive Router and a network Extender from the same manufacturer. I won't go into all the reasons but it was unsatisfactory, so I decided to try something different. I went back to my old Router that had worked well but just did not have the coverage we needed and turned the WiFi OFF. Then I connected the Router via Ethernet to a Plume "pod" configured to passthorugh the routing information and placed additional "pods" scattered in rooms around the house. From there on setup was completely automatic. I won't go into how the Plume network works but the coverage is amazingly uniform and even more amazingly fast. Plume markets directly to the public and I don't know if they ship to the UK but it might be a solution for you.

FULL DISCLOSURE: I have no relationship, pecuniary or otherwise, with Plume WiFi other than that of satisfied customer.


If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein