Hmmmm, there might be a contract in place already but the devil is in the detail and you'd need to wade through the many pages of small print. Based on your posts here, at best it seems like shoddy practice. Bikesure are (unless the small print says otherwise) the agent for Aegres who I assume are the insurer/underwriter, so it's reasonable for you to rely in good faith on the price you were given and paid. Arguably if there was a mistake between Bikesure and Aegres they should sort it between them as the one person in this triangel not at fault is you. However the harsh reality is you need insurance and if they say you dont have any without stumping up an extra £400 you are (to say the least) disadvantaged. You could pay the extra under protest then seek to recover it from them as a breach but that would take time energy and hassle. Although their terms will say they can charge extra in some circumstances, I'm not sure that doing so based on their cockup is reasonable.
Do you have legal expenses insurance? You may have access to free legal advice by phone. Even if your legal expenses cover is under the new policy, chances are the legal expenses is a bolt on by a separate underwriter so you wouldn't be asking the legal expenses bods to advise against themselves IYSWIM. However, there would still be a commercial connection between the legal expenses insurer and Bikesure/Aegres, so they might not advise on this. You might have legal expenses under a home or other insurance which might help. All a PITA though.
Another issue for you is that it is commonly accepted that the sweet spot for buying insurance is ~26 days before you need the cover - the MSE website would confirm more specifically. If you are already past that timescale, your ability to buy at competitive rates is already compromised through no fault of yours.
Probably worth a complaint whatever the outcome. If not satisfied with the response, you can escalate to the Ombudsman. Not a fast process but if you are calm and measured, you have a decent shout at your complaint being upheld and some compo awarded. One difficulty will be showing what premium you might have got in the sweet spot against what you can now get much closer to renewal.
You might want to offer Bikesure that if they will honour the original price but only for (say) a month for you to get cover elsewhere without the sweet spot penalty, you will toddle off elsewhere and might save some £££ meantime. I doubt they will take you up but it may be good to put that offer in with any referral to the ombudsman to show you made a very reasonable offer to resolve without Bikesure etc being committed to 12 months cover at the original price which they quoted.
Make notes NOW of your calls with them including times and dates. Email those notes to yourself so you can show they are contemporaneous. Ask for copies of the calls using a Subject Access Request too.
PITA for you whichever way you slice it. Good luck.
