I don't know any cinemas, but I know that the Odeon video rental place has lots of Hungarian movies with English subtitles on DVD.

If you search their catalogue ( http://www.odeon.hu/kat.phtml ) and set the "nemzet" field to Hungarian and the "DVD felirat" filed to Angol you'll get the list.

Odeon has four locations, inside four movie theaters:

Duna: XIII. Hollán E.u.7.

Corvin: VIII. Corvin köz 1.

Puskin: V. Kossuth L.u.18.

Taban: I. Krisztina krt. 87-89.