A single tunnel sounds like a really bad idea, but a series of underpasses to divert traffic from town centres would be helpful, but it unlikely to free up much space for development or pedestrianisation.
In our area I could imagine a tunnel starting in Dulwich and continuing to Stanstead Road, with another starting close to St Dunstans and continuing to Brownhill Road. Another short tunnel at St Mildred would past the railway more efficiently.
Further tunnels could assist traffic flow at Tulse Hill, A23 junction, the whole of Clapham with no exit until after Wandsworth (to allow for junction with the A3), then after a short tunnel under Putney I would be inclined to take a tunnel straight under Barnes to join with the M4.
In many ways this plan is an acceptance that the idea of radial rail routes for London was never as useful as was claimed. Linking east and west London by orbital rail has done nothing to reduce traffic on the South Circular as cars are still the easiest way to get to most areas of SW London from SE London (and the same is true in North London).
My view is that radial (or more importantly bisecting) railways are the future of London transportation. Thameslink, Crossrail, and Crossrail2 all conform to this vision, but the vision seems to stop here. What we need is the bakerloo line extension (via Forest Hill to Beckenham), Victoria line extension (via Streatham to Croydon), and a new branch of the Jubilee line running from North Greenwich down to Lewisham, Catford, and Bromley. all these should be underground and will be cheaper than £30bn spent putting roads into tunnels.