Hang on, you said "investments" with Lloyds (and subsidiaries) do you mean investments or deposits?
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Afaik the gov didn't have to pay out (directly) for any uk banks under the compensation scheme (the one that guarantees your deposits up to £50k at the time now more with various allowances for joint accounts etc).
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If you invested via a uk bank then the gov never did and never should guarantee that money.
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This actually leads me onto a proposal for making banking simpler and safer.
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Essentially you can have a "guaranteed" account, like any other bank account, cards, chequer book, online, standing orders etc, except that any money in the account is guaranteed by the uk gov. These accounts would have a logo or seal or something to make it crystal clear to customers. Banks who offered this would have to be "rig fenced", i.e. independent entities that only dealt in these accounts. They would be vetted and would also have social obligations, e.g. "homeless" accounts, debt advice etc. The deposits would be deposited with gov bonds paying whatever the interest rate was (i.e. low). In order to make money these banks would charge for accounts and services (except for the "social" accounts they are bound to provide). Effectively the banks would work like a front for premium bonds with all the services of a current account.
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If you wished a higher return those banks could offer products with their explicitly un guaranteed sister bank, like mortgages, loans, investments etc. all via the same "interface".
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So I might bank with Lloyds, have an account with "approved Lloyds" for £10 a month but also a chunk of cash in the "uk mortgage deposit" account with "Lloyds Investments (un guaranteed)" paying 2% and some more with the "risky" account paying 6% plus a few share packages.
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This would give the public access to a solid, reliable, vetted bank where there money is as safe as can be, vulnerable groups would get access to banking, the gov would get access to more lending. People with an appetite for risk could also be served, but if an "investment" bank went pop, the investors would be left to swing because they were investors not depositors.
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Of course some of the banks did blur the lines between deposit and investment meaning people thought their money was safe when it was in fact invested and at risk. An acquaintance of mine lost a huge amount when their savings, invested in supposed 'ultra safe' bonds, turned out to be Lehman bros bonds.