I'm thinking not for the medical side of things, but maybe for the value of the bike I'd be taking?
Whaddya think.
the vast majority of travel insurance policies have a single item limit of around £250 (and around £1500 max total), so you're bike aint likely to be covered even with cycling on as an activity.
The best thing is usually to speak to your home insurance provider about it
Check your household insurance, always a good idea to phone and speak to your insurer, as insurers can/will change the T & C's. I done this last year and I was fully covered whilst on holiday.
My easyjet insurance covered me specificaly for mountinbiking, the £250 (or whatever it was) didnt bother me as I was on a 456 with s/h forks so the odds of doing >£250 of damage to it were slim to none! And if I did I'd have claimed seperately for the frame/forks/wheels/bits as it was a custom build (no doubt they'd argue the opposite though).
Note: your E111 (or whatever the new card is called) wont cover everything, IIRC things like Search and Rescue, Air Ambulance etc which are NGO's can add up to a huge bill, ditto repatriation so well worth checking your covered for stuff like that.