What should I look out for?
Don't confuse new for old policies with indemnity policies, also known as 'wear and tear' policies. The latter take use and damage into account, so will replace items at their current second-hand value taking into account depreciation.
That means if you claim for a washing machine that was three years old, your insurance provider will pay for a three-year-old washing machine, not a brand-new one.
You should also read the small print to make sure you know exactly what is and isn't included.