I am told by Allianz that they will not provide me with an Annual - Multi-Trip Travel policy. This refusal has nothing to do with medical criteria but is based solely on age! And yes, I can effect a policy elsewhere and only tried Allianz on the direction of Irish Life Health, who told me that I would get a 20% discount !!!
At this time it seems they are not interested in quoting for your business, that is their right as it is your own right to go elsewhere, I am sure you will happily exercise your right and extend that right so you exclude them for any motor or home cover you may require.
Try blueinsurance. They are reasonable and give a discount if you have health insurance. Make sure to read the t&c's and disclose any existing medical issues you have to their medical line or you won't be covered.