I hope this link will be helpful http://www.electiondataarchive.org/datacenter-gred.html 

Thank you! Therer are a lot of countries. I'll take a look!

European Community headquarters.

Thank you. Do you know any specific department, institution?

You can freely download geographic information (shape files etc.) of German Bundestag constituencies here:

https://www.bundeswahlleiter.de/en/bundestagswahlen/BTW_BUND_09/wahlkreiseinteilung/kartogaphische_darstellung.html

For the UK, a complete data set with administrative/electoral boundaries is available here:

https://data.gov.uk/dataset/boundary-line

To find geographic data sets for other countries, I suggest you find out how the administrative unit that you are interested in is called in its native language and then use that name as search term, possibly in conjuction with the term shapefile. For example, for French legislative constituencies try

circonscriptions legislatives shapefile

for Romania and Republic of Moldova: http://polito.ubbcluj.ro/romanianelectoraldata/

best,

cosmin

For Germany, you can look at the websites for the Bundestag and the sixteen lander in the country. 

For Hungary: http://www.valasztas.hu/en/ogyv2014/416/416_0_index.html

and around this.