There are additional traffic lights on the blackwall tunnel further in and a slip road out that can be used for overheight vehicles. I do remember having a 10-15 minute wait once while they sorted things out when a lorry driver got caught.
I'd have a feeling there are automated signs prior to the tunnel (or at least used to be) but I've not been through the tunnel for a year or so and things will have changed with the Silvertown tunnel opening.
I have seen someone not paying attention at the Rotherhithe tunnel and the roof of their van was a mess (and they're going to pick up a fine probably due to restrictions, the 2 tonnes gross weight limit is lower than a lot of van drivers expect)
I'd have a feeling there are automated signs prior to the tunnel (or at least used to be) but I've not been through the tunnel for a year or so and things will have changed with the Silvertown tunnel opening.
I have seen someone not paying attention at the Rotherhithe tunnel and the roof of their van was a mess (and they're going to pick up a fine probably due to restrictions, the 2 tonnes gross weight limit is lower than a lot of van drivers expect)
Edit there were: https://maps.app.goo.gl/MP7fkhS394DJPQaZ9 If you zoom in you can see the overheight vehicle warning.