You have two problems; proving that your wife is entitled to the estate, and proving these accounts are in fact part of the estate.
The first should be relatively easy. Whoever acted as executor must have kept records, and may with luck still have copies (particularly if it was a solicitor, who billed for every action). At worst, every will proved in England and Wales has to be registered with the Probate Registry, and it is likely that a will from ten years ago is retrievable electronically (similar conditions hold if the estate was distributed in Scotland or Germany, though the details will be different). This will presumably show your wife as either sole or residuary legatee; if not, then she is not entitled to the money, so your quest ends.
If successful, you then have to prove that the Michael Doe who opened the account is the same as the Johannes Doe whose estate is in question. Without going into more detail than is appropriate here, there's no way to tell whether the documents you have (and that presumably prompted this question) will be enough. A few points:
Technically, only the executor has the right to pursue these accounts; if he is still around, it may be simplest for him to write a letter assigning all rights in the estate to your wife as legatee.
It is not enough to prove that Johannes also went by the name of Michael; you have to show that the two are the same (after all, Doe is a common name...)
The executor must have advertised for all debtors and creditors of the estate to contact him. If you can find a copy of the advertisement, and are lucky enough that it refers either to Michael Doe or Johannes Doe also known as Michael, then the bank
is probably at fault for not complying. There will certainly not be any compensation due, but it may be of help with the next point.
The bank has no interest in helping you, and will try to put you off at every turn. There is no upside for them whatever happens, but a lot of work for somebody and possible embarrassment if (for example) they have treated this as a dormant account when it was not. You will have to keep prodding; you may have to ask the Banking Ombudsman to intervene or go to court.
Even if you are successful, you will certainly have to indemnify the bank, and perhaps take out insurance, in case the real Michael Doe contacts the bank after you have been paid and asks for his money back.
Once you have the will and as much documentation as you can find, I would recommend consulting a solicitor (the one who drew up the will and/or was executor would be best) to ask whether this pursuit is likely to be worth it. If the accounts will not cover a consultation fee, it is definitely best to forget them.