JJ, I assume that you used an Insurance Broker to arrange your insurance cover, and that both your house and car insurance are with the same insurer.
When you first dealt with the broker you should have received an Initial Disclosure Document headed 'Key Facts'. The layout of this document is stipulated by the Financial Conduct Authority. Under heading No 2, Whose products do we offer? should be either 3 tick boxes, of which only one must be ticked, as follows:
We offer products from a range of insurers (can be followed by insurance type)
We only offer products from a limited number of insurers (can be followed by insurance type) Ask us for a list of insurers we offer insurance from.
We only offer products from a single insurer (or name of insurance undertaking)
or if there are no tick boxes, the following wording instead:
We only offer products from a single insurer.
or alternatively:
We only offer our own products for [list the types of policies].
Under heading number 3, Which service will we provide you with?, should be 2 tick boxes, one of which should be ticked, as follows:
We will advise and make a recommendation for you after we have assessed your needs [for] [list the types of policies].
and
You will not receive advice or a recommendation from us [for] [list the types of policies]. We may ask some questions to narrow down the selection of products that we will provide details on. You will then need to make your own
choice about how to proceed.
If you haven't got a recent copy of the this document, ask your broker for a duplicate. Hopefully they will have ticked the first box under both headings, in which case they are looking after your interests.
They should also have provided you with a 'Demands and Needs' statement when you took out each insurance, although if I remember correctly you were rushing around recently to renew your car insurance, therefore this may not apply. I would also ask them for a copy of their Retail Customer 'Terms of Business' document, which could also disclose whether they are a 'tied agent', working for one insurer, or if they research the market to obtain the best product for your needs, and may indicate where they derive their commission from.
(A bit long winded, but I had to try to remember this from when I was a consultant to various insurance brokers and drew up/corrected their required documentation).