Institutions Research

In my research of institutions I think that 20th Century Fox would distribute our movie, as they have a great line-up superhero and action movies:
Deadpool
Batman
The Mark of Zorro
Zorro The Gay Blade
2 Power Rangers Movies
Daredevil
The League of Extraordinary Gentlemen
Elektra
Fantastic 4
and 7 X-men films

Another possibility would be Columbia Pictures as they have had some superhero movies and some good comedy movies:

Mr.Deeds
Spider Man
Spider Man 2
Spider Man 3
Bad Boys II
The Longest Yard
Ghost Rider
Big Daddy

Below is some points that Aidan has made:

Distributor

It is unlikely that our film would be distributed by a major American distributor; this small production would be unlikely to interest them. It is unlikely that a major cinema release would be possible; getting a film into cinemas is expensive and difficult, with the major American companies able to buy out most cinemas and push out low budget British production like ours. Therefore, our film would likely be distributed by a small, British company, possibly via an alternative medium.

An example of such a company would be ChannelFlip. ChannelFlip is a small but relatively well known company and YouTube network who, among other things, ran the YouTube channel The Multiverse until the summer of 2014 when they lost funding from YouTube. Many shows from this channel, such as Knighthood and Decoy, are continuing on different media platforms. ChannelFlip often works on small and experimental projects, such as Ashens and the Quest for the GameChild, providing funding and good connections to help production. They are known for "geek flavoured entertainment" such as fantasy, science fiction and superhero related comedy. This is the kind of company who would likely distribute our film.

Aiden brings up some good points here, even though Columbia and 20th Century Fox do have some similar movies in there lineup of films they are too big of a company to even consider funding and/or distributing our movie so we would most likely need to go with a production company who would be able to get our movie out there but be small enough to actually take our film on board.