scottish_ppl
You can change a broker anytime (just write to the new one a letter authorising them to take over the business).
But if your insurance is done by a broker who went via another broker, the final broker will not want to look like they cut somebody else out of the deal. In theory you could but in practice you are probably stuffed for good unless you terminate the cover for a few months and then re-apply. Luckily you aren't usually paying extra for it; they split the commission between them.
The downside of a chain of brokers is that claims will take longer to process. And if a claim takes place soon after you first sign up, there can be a delay of several months because the underwriter won't pay anything until he has received the first premium cheque, and it is not unusual for some brokers to hold on to your money for 60-90 days.