The short answer
Begin several months before the fixed period ends. Ask your lender what rate and repayment will apply, then compare staying, refixing and switching. Include legal, valuation, cashback and break costs rather than comparing headline rates alone.
A fixed-rate expiry can change the monthly repayment automatically if you do nothing. The earlier you understand the options, the more time you have to gather documents and compare properly.
Your review checklist
A broker may help compare lenders, but ask which lenders they cover and how they are paid. If you stay with the existing lender, you should still understand why that option suits your circumstances.