Please tell us your route to the mini-roundabout on Blonk Street, it's important in order to assess signage adequacy.
If you click the google maps link in my first post you can see where I arrived at the roundabout. Spin around 180 degrees and you can see where I came from - the access road to the carparks (I had been parked in the NCP carpark).
Yes, I understand that, but did you come up Blonk Street and across the river bridge ? If you did you'd have seen no Bus Gate signs until you came out of the side service road and turned back onto Blonk St and crossed the river. However, if you had come up Blonk Street from Exchange Place, you would have seen this advance sign: -
https://maps.app.goo.gl/pm2gPw2WSU31SnxPASo your route is important if you are to write a credible appeal argument for an adjudicator. If you came up from Exchange Place, your argument of not seeing signs is clearly not credibleas you see the advance sign, then the bus gate signs straight ahead. You now have to submit representations to Sheffield City Council but whatever you say, you'll just get a Foib-Off letter.
Bad/missing/inadequate signs cases normally only get an unbiased hearing at the adjudicators. So the $64k question is, are you prepared to take them to the Traffic Penalty Tribunal and risk the full PCN penalty ?