Whether someone has or hasn't had this problem in Bulgaria probably won't shed much light, as such a form from just one UK organisation isn't possible to procure (as far as I know).
So it seems to me that your commonsense options are as follows:-
1. Convince the 'institute' (What's it for, btw, if you don't mind me asking?) that it's just not possible and invite them to research the procurement situation in the UK themselves.
2. Convince them to accept some alternative of their (realistic) choosing - letter from bank/previous employer/police or whatever.
3. Go along with their request and just knock the requested letter up yourself. This is the normal way it is done in Russia - I have even been asked by some people to proof-read letters that they have written related to job applications, supposedly from their referees!!
Good luck anyway!