In the UK the use and processing is governed by the Data Protection Act.. This is a law that requires companies to use and store your data only for relevant specific purposes and under strict regulations. If the company has a relevant reason for having your complete medical history (a real reason, not just in their opinion) they can make you give it. If not they cannot. I am not a lawyer but in my view the company has no legitimate reason to ask for your medical records, and I have never encountered a company in the UK or elsewhere that asked for them, even when private insurance is offered. Sending your records direct to the insurance company (who are forbidden from passing them on without your consent) is normal, and most don't even need that. There is huge potential for abuse if your employer had unrestricted access to your medical records.
In your place I woul research the Data Protection Act a little. Then I would write to the company and ask specifically what use they will be putting the data to and what restrictions they have on its use under the DPA, including who they might be provided to. Make it clear you are aware of the DPA restrictions. Say you are happy to provide your medical records to medical practitioners.
If I were you, unless the company provides a compelling reason to have the records (and I can't think of a valid one) I would decline. However be aware that this is a high risk strategy as the company may rescind their job offer, and while my amateur opinion is that would be illegal, even if it were true proving it would be very hard.
You might consider consulting a UK lawyer. If a lawyer were to tell you that making your employment conditional on medical records was illegal, passing that on to the company might convince them to drop the request. However a company prepared to ask for illegal information is probably shady in other ways.
According to comments the employer is asking only that you send them the records so that they can be forwarded to the insurer. In that case they have some legitimacy. However I would still be cautious. My preference would be to tell the employer that you will forward the records directly to the insurer. I would also contact the insurer to verify that they absolutely require the records rather than just would like them (again in my experience most insurers don't need them). If they do then check the form for a statement saying that they will not forward the records to anyone without your consent (this is normal practice) and mail the records directly to them. Thank the employer for their kind offer to do the forwarding, but say you prefer to deal with the insurer directly. At the very least you should put the records and the form in a sealed envelope addressed to the insurance company and marked "confidential" and send it to your employer for forwarding.