Sorry but I'm confused by who the other people are. Who are the other people who might have keys? Who was last heard of living rough in France? Are there other living siblings?
How did the police get keys? Did they break in to discover the body and take away a set of keys at that time? Possibly after gaining access they had a locksmith change the locks and the locksmith left all the new keys with the police?
IF there is no Will (ie he died Intestate), and IF the brother who has died in the Barbican has no living parents or children, and IF your friend is the only surving sibling then your friend would inherit the property and the deceased's whole estate. And she would be the person who could apply for Probate and would then have the authority to deal with his Estate. If there are other living siblings the estate is shared equally between them.
But she is going to struggle with this if she doesn't "do computers". Most things involving administering an Estate have to be done online. If it turns out she is the closest relative to handle the Estate if there is no Will (or if there is a Will that names her as Executor) she might be best advised to employ a firm of solicitors to deal with it all. Especially if, as your post hints, there may be another sibling somewhere entitled to a share of an intestate estate but who can't be found. If her late brother owned a Barbican flat outright (no mortgage/loan to pay off) the Estate will well be able to afford solicitors' fees. Barbican flats are expensive! Online sites like Zoopla will give a rough idea of current value.
Of course she doesn't know if there is a Will yet, she needs to gain access. She should ask the police if they can let her in. Ask neighbours or any known friends if they have a key (unless the locks have been changed).
Does she know who her brother's solicitor is? I'm guessing not, but if she does she could ask them if they have the Will. There's a private company called The National Wills Register who store Wills. She could check if they hold her brother's.
Is an Inquest being held? If so the death can't be formally registered until after the Inquest but the Coroner should issue her with an interim death certificate called a "CORONER'S CERTIFICATE OF THE FACT OF DEATH" which she can use to administer the Estate in the meantime.
She can check the actual ownership position of the flat (and if there are are any mortgages or charges) at the Land Registry. She'd need to set up an account first and there's a £7 fee but it's straightforward. The document she needs is the Title Register (don't need Title Plan).
https://www.gov.uk/search-property-information-land-registry
