Yes, unfortunately you can’t claim BW rights by historic use by bikes alone. It however doesn’t preclude a claim by horse riders, but seeing as it doesn’t say “no bikes / horses”, just “no bikes” they probably will focus their time / effort elsewhere.
Having had a squint at the route (~SJ 4885 5294) the cycle path is marked as ‘other route with public access’. For some reason the landowners have withdrawn their permission for just bikes, which they are entitled to do.
I’d ring them up in the morning and ask very nicely what their plans for an alternative route is, restricting it after ~20 years would make me very miffed TBH (or just inclined to ignore them)