Nottingham local here.
One of the biggest issues at Nottingham is all the nearby local stations. All the stations on the Newark line, the Robin Hood line and the Skegness line are mostly all small stations, with just one ticket machine.
There's definitely a culture of 'pay-on-board' from all of these stations: it's not that people specifically want to fare evade and will pay up when the guard comes, but more often than not if it's a busy peak time service with all the stops the guard won't have time to come round, so they don't pay.
Everyone knows that you can just leave Nottingham bypassing the barriers, so if you don't manage to buy a ticket you can just leave. These people are also aware you have to buy on board, but no-one will ever challenge someone doing that on these routes.
The way I would tackle this is to introduce ticket barriers on the bridge, but let anyone who needs the RoW through. The majority of these people will be travelling to Nottingham on the Outward journey, and back from on the return. Therefore, they will always buy a return ticket as it would be impossible to leave the station without a ticket. Sure, it'd be quite easy to enter by just asking to use the RoW but 1) these people will have bought returns which are normally 10p more expensive than a single and 2) these people aren't fare evaders and only don't pay purely because it's easier not to. If there's a deterrent of a barrier, they'll just buy a ticket!