Changing unusual foreign currencies in London

Did you try your bank? HSBC, for example, will convert any currency to your local currency if you are an account holder. The rates are quite good and they don't charge a fee. The downside is that they have minimum amounts for each currency type (usually around $50 here in the US) and they don't usually convert coins.

Edit:

Also, if one branch of a bank says they can't do it, it doesn't mean that all branches of that bank can't do it. A friend of mine recently had to exchange some Hungarian Forints and Czech Koruna here in the States. He went to his bank, PNC, and they told him that they could only convert from eight major currencies. He then went to a different branch of PNC (in a more upscale area of town) and they said that they could convert any type of currency. They have some "currency specialists" to whom they send the money who verify that the notes are legit. Once they are confirmed legitimate, they do the conversion. The process can take up to 6 weeks (I'm not sure how long it actually took for my friend).

As an aside, my friend noted how bad the bank tellers were at geography: The first bank teller insisted that "Hungaria" is not a country, and the second said, "Does the Czech Republic still exist? I thought it's part of Russia now..."

Use a website where travellers meet, perhaps Couchsurfing or Lonely Planet Thorn Tree. Advertise that you have some unusual currency you wish to change at the current official rate with no overhead or fee, just direct traveler to traveler to somebody about to go to the destinations you just returned from. Arrange a time and place to meet (not in the forum where everybody can see just in case).

You'll probably have lots more to chat about when you meet up to exchange money and unless you've got ten grand worth of Tenge or something you shouldn't have to worry about the Central Asian mob turning up to shake you down (-;

I've used Thomas Exchange Global when I was looking for better rates to sell currencies in London. On their web site they list Kazakhstan Tenge, but not the other three. However, they say to call them for exchange rates of currencies not listed, so you may be able to exchange your other currencies. They have locations on the Strand, Liverpool Street, Victoria and Hammersmith.

There is also Thomas Exchange. They do not have any of your currencies listed on their website, but have confirmed that they will exchange all of them (via Paul Nelson's answer here). They have locations near Oxford Circus and Liverpool Street.

Talk to embassies of those countries. They might know where to buy/sell the currency. Is there a big official central bank you can go to? They might do everything? (Or they might only change your pound notes to pound coins).

It looks like you've tried all the likely suspects.

The Post Office website has a section on selling back currency which lists all the currencies they'll buy from you. As you've discovered, none of your four are on that list... Bigger branches of Marks and Spencers are normally worth checking for foreign exchange, as they often do a good rate. Alas their list lacks your currencies too.

As you're in London, I'd suggest you try to find a restaurant or shop run by people of each nationality, and see if they'd be interested. That'd likely depend on how much you have, and how often the staff there return to see family, but there's a fair chance they could be interested at the right exchange rate (FSVO right = right for them!). This option also has the bonus that you'll be able to pick up some food in the style you've just been enjoying!

Unless the value is really high, you can sell the notes on eBay. Someone will be willing to pay a small amount of money for some exotic bank notes. Since this will be just collectors buying for the novelty value, you won't get too much.