The Financial Services Compensation Scheme (FSCS) covers bank, building societies and investment accounts, and will pay compensation if the holding institution goes bust.
Updated August 2018
The Financial Services Compensation Scheme (FSCS) covers bank, building societies and investment accounts. If a bank goes bust, the FSCS will pay compensation of up to £85,000 per person per bank to cover any losses (or up to £1m if the money is there temporarily the proceeds from a house sale, say).
So if you have substantial cash savings, you may want to have accounts with more than one financial institution (and if you do split your savings, be aware that many bank brands share the same bank licence, so check you are genuinely saving with two separate institutions).
As for brokers, if yours goes bust (assuming it is based in the UK overseas brokers will fall under different compensation schemes, assuming there is one at all) and there is a shortfall in client assets ie, money that should be in a segregated account turns out not to be then the FSCS will pay out up to £50,000 per client (not per account) to top up whatever can be recovered from the broker.
So if a broker owes you £70,000, but you only get back £40,000, you should be entitled to another £30,000 from the FSCS. However, if you have two accounts with the same broker holding £70,000 and £80,000 and you get back £40,000 in each, the FSCS will pay you a maximum of £50,000 leaving you £20,000 short.
You can choose to make an FSCS claim after getting some money back from the insolvent broker, or before it pays out anything. When you make a claim, the FSCS takes over your claim against the company. So, if you are owed £70,000, the FSCS will pay £50,000 and make a claim for £70,000. If it gets £15,000, it passes all of that onto you. If it gets £30,000, it pays you £20,000 meaning you get all your money back and retains the remaining £10,000 to recover some of its losses.
For more details, see FSCS.org.uk.