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)

Edit there were: https://maps.app.goo.gl/MP7fkhS394DJPQaZ9 If you zoom in you can see the overheight vehicle warning.

I presume the Blackwall one is that unlit LED sign just at the start of the off-ramp. Then there's another set of height detectors on the same post to catch out anyone who's still not paying attention.

I question who approved that the main lanes ahead of your link have 2.8m/9ft limits but the police warning says vehicles over 4m/13ft will be stopped. Can I take my 10ft truck through or not?

I'm starting to feel a tiny bit of sympathy for drivers that get confused by this.