It certainly is a shame Swanick don't allow work experience people to have a look anymore. LHR tower I can understand saying no, but ACC seems the perfect opportunity for someone with an interest to gain some insight.
I spent a week at MAN ACC during mid 90s. Got to sit and listen in at every position, in the tower, downstairs with the approach controllers, amazing stuff. It was the final push that confirmed I wanted a career in aviation, no matter what. All organised by a family friend who was a controller there, no security red tape, just bring a passport, listen to the briefing from the SATCO, use a bit of common sense and shadow an ATCO for the day. It's a real shame all that is no longer possible.