Free Traffic Legal Advice

Sorry, but no good without some hard facts. Please read this and update your thread accordingly: -
https://www.ftla.uk/civil-penalty-charge-notices-(councils-tfl-and-so-on)/read-this-first-before-posting-your-case!-this-section-is-for-council-tfl-dartme/

So here is the tunnel approach on Branch Road: -
https://maps.app.goo.gl/gFbLzEG6PDENeChp7
The sign shows a weight limit of 2 tonnes. Did you not notice this sign ?
Also there is a sign on the approach from the eastern direction on Commercial ROAD : -
https://maps.app.goo.gl/gFbLzEG6PDENeChp7
and another sign proceeding in the opposite direction: -
https://maps.app.goo.gl/v2aTxppsfZvVRXxj8
Then having made the turn, this sign: -
https://maps.app.goo.gl/o2hTRR6bi8vmp9Yj6

So basically you have to argue against these signs ! As a commercial van driver, you are expected to be aware of weight limits. 

Having said the above, there may be a 'technical' appeal argument based on TfL's mismanagement of the enforcement process. The first thing to do, however, is ring them up and ask for their video, (sent as a DVD via post).  They then suspend enforcement for 2 weeks giving us time to look at your case without being rushed.