John Lewis, expensive bikes aren't covered for free but the premium was cheap to specify them and the policy is underwritten by Alliansz
No it's not, it's underwritten by RSA (More Than), but your point still stands. None of the big companies will have affinity relationships with little insurers like you say, so I'd not worry. You don't deal with John Lewis, you deal with RSA (who just say "thank you for calling John Lewis"), no small insurer will have the facilities to support that.
I just renewed with M&S - be honest about the value of the bikes though, I said £4k on one and it added £100 to the premium, when I said it was actually £3800 it took £40 of that off - like it's exponential.
I paid £250 in the end with two bikes over the £2k. New business like for like quote with M&S was £700 - Axa have obviously been burned with lots of high value bike theft claims, hardly surprising!