I can think of two or three methods of doing this.
The full medical is one approach, but I think you'd end up doing this privately and the cost through BUPA is £300 or so.
Secondly, you should be able to get hold of your medical file from your doctor which will make answering the questions easier.
Thirdly, life brokers have access to life insurance where the health questions are answered over the telephone to outsourced underwriters. Having said that, alot of brokers avoid it, because the commission is reduced as the costs are higher, but in general the system is good. The telephone calls are recorded, meaning that there is no wriggle room for you nor the insurer. This may allay your fears, especially in conjunction with part 2.
Hope this helps
Adrian