It really depends on the role. In my role I work across all brands and products within our Personal Lines team (to customers). We also have a commercial side of the business which focuses on all products Business to Business.
Brand managers tend to work on one brand and product (i.e. Direct Line Motor Insurance).
Although in a role you might only work day to day on one brand and product, you are regularly exposed to the goings on in all of them. We have a lot of cross portfolio sessions, and as a marketing team work closely to share learning's and insights across the products.
Hope that answers your question, however if you have any further questions feel free to drop me a note.
Thank you for your feedback!