That’s interesting. But misses a rather crucial point that Birmingham has a rather substantial commuter rail network that’s functions much like a metro. Which rather negates much of the study.
That report claims a 33% shortfall in productivity due to Birmingham's lack of more than one tram/metro corridor, but Manchester, with its extensive tram network, would be considered by them to have a 20% shortfall. And Sheffield and Newcastle area with their tram/metro systems perform badly, with Bradford being the only city analysed that's further from the French trend line.
And Portsmouth and Bristol are the two English cities which, by their measure, are over-performers. Even the suburban rail in those cities is pretty bad coverage- and quality-wise: it's all buses and cars there.
It's terrible analysis, even with the assumptions they are making about bigger is better (most French cities are shown to have similar GDP/capita, but the outliers tip the graph to make it look like bigger is better), to look at just one other city - Lyon, and not also look at Manchester (as a similarly sized UK city to Birmingham and Lyon, that does slightly better than Brum and a lot worse than Lyon).
And they don't look down the line - there's a big cluster of similar-sized cities with Edinburgh, Bristol, Portsmouth and Glasgow way above the trend line, Nice, Nantes, Strasbourg, Rennes and Grenoble a little way above the trend line, Rouen on the line, Cardiff, Leicester, Nottingham, Montpellier, Saint-Etienne and Liverpool a little way below, and Toulon, Bradford, Sheffield and Newcastle some way below. That's where your thesis has to be produced, not by dealing with a comparison between just two outliers...