We have an area that is very well served by fire exits, there is a desire to gain back some wall space for freezer storage by placing them in front of one of the exit doors.

I'm confident that without one door we can still meet the necessary travel distance requirements.

Is it sufficient to simply remove the exit signage and revise our Fire Risk Assessment or do we need to involve Building Control?

I'm in agreement with Invictus and it should come out of your risk assessment, but I would not just remove the exit sign I would review the exit signage. As this exit is now no longer available you may need additional signage directing people to the escape route. And I do stress MAY as clearly I have never seen your site.

Yes it can be done, no fire certificates nowadays so your fire risk assessment is your responsibility.

Agree with others, revise your Evac plans and don't forget to remove all signage that points to that exit.

Some people forget that one.