So many excellent replies...
Although I did not specify Mount Pleasant as the place within Clerkenwell that would be the optimal site for a new Underground station, this is the location that I had in mind. Of course I would expect all works to respect the mothballed (and now touristic) sections of Mail Rail so that Mail Rail could be reopened, if ever the bean counters saw fit - or were replaced with people who believe that Mail Rail is a valuable asset and extended it as required.
I am aware of the proposed subsurface station between Farringdon and Kings Cross but how feasible would it be? Especially with the Widened Lines /
Thameslink trains running so close on one side? Oh and also, how long would the disruption to services be whilst the route (both lines - subsurface and TL) are closed for the major earthworks?
When I visited Mail Rail my walk from Kings Cross station to Mount Pleasant took longer than just the suggested '5 - 10 minutes'!
Yes I am being a crayonista, but not wholly ... London Transport wanted to extend the Piccadilly line from Aldwych to Waterloo and they even got the necessary legal powers to build this. I suppose that Parliament will have imposed a time limit for the works to be completed (its happened elsewhere with other extensions) and that therefore these powers will have now lapsed.
My thinking process has always been along the theme of having an inner city subterranean rail link which would have cost much time, money and effort to build just sitting there not being used,,, so what could be done to make productive use of it?
The Waterloo idea comes from it always having been a London Transport desire and the Clerkenwell idea coming from this area being unserved and wanting to see how to remedy this.
The idea of then going on to Victoria comes from when I've tried to make that very journey, having travelled to Waterloo via the Waterloo & City Line and then visiting the former Ian Allan bookshop. I ended up going by bus - it seemed to take ages (probably would have been quicker to go by train, changing at Embankment) . It seemed (still seems) crazy that such important London terminus stations do not have a proper railway link. I understand about how (when it was built) it was decided that the Metropolitan District Railway could not serve Waterloo station - because Waterloo station was south of the river (Thames). Btw, my journey did not pass through Clapham Junction and at no time did I ever consider taking a train that way. Train fares on the Southern are noticeably higher than other routes.
Although it would make sense to include a connection with the Waterloo and City line I would only expect this to be used for empty stock transfers and to end the use of the crane. The already existing link with the Piccadilly line at Holborn would also be retained, but again only for empty stock transfers.
I did not advocate a fully Circle service because there are already good enough connections between the Kings Cross / St Pancras / Euston area and Paddington. But I have thought about 'beyond Victoria'.
One option would be to end here!
Another would be to go to Marylebone via Marble Arch, another would be to Paddington, with the platforms directly linked to Paddington at its northern end and Lancaster Gate at its southern end. In theory it would be nice to see this routed via Kensington Gore / Royal Albert Hall, as this is another area that London's existing railways do not serve. But the large amount of parkland here suggests that there would not be sufficient passengers to justify a station, whilst nearby South Kensington is just crying out for greater capacity - and has at least one station tunnel that is already built - but not used! In some ways going to South Kensington would help relieve the overcrowded central London portion of the Piccadilly line, something that Crossrail won't do.
(The self-inflicted injuries causing the overcrowding of the suburban north London Piccadilly line in the Wood Green area are outside the scope of this plan - all I will say is that I see this as a direct result of the idiotic closure of two perfectly good rail services via Noel Park & Wood Green and Muswell Hill.)
Another option would be to revisit a WW2 plan for tube trains to Yeading, which would make this a very different type of service. But its also unlikely to become a reality - if only because the bean counters will moan about it possibly abstracting passengers from Crossrail line 1. As we know, the proposed tramway along the same alignment also failed...
I agree that the rise of the Uber style of mini-cab has caused an increase in congestion, although the mere fact that these private hire vehicles survive financially suggests that London's existing public transports are not meeting everyone's transport needs. I dislike the idea of simply banning private cars, it makes me think of authoritarian police states, for instance I understand that the Nazis banned private cars in Paris after invading the city. I used to know someone who lived in St Johns Wood who voluntarily gave up his car because by the time he paid all the taxes, insurance and parking fees it was cheaper to use taxis the few times that he actually needed 'door to door' travel. I would like to see financial incentives for people to do likewise.
I went to school on the Northern line in the 1970s and travelled on both 1938 & 1972 tube stock trains. Happy memories! I wish it were possible for a museum railway to take this train and fit batteries so that it could be travelled in.
Yes, CGI has really come of age in recent years. Its amazing what can be done, although in the old days the adopted solution was to build a replica film set, eg: House of Commons for films depicting the interior of the HoC. I think everyone here will have heard about how the pop music group ABBA is using CGI to make themselves look umpteen years younger than they now are - but what is really significant is that they are doing it in 'real time'. When does CGI become 'too much' - at least with feature films one 'sort of' expects some of what is seen to be CGI, how would we know if it started being used where its not expected, eg the TV news?
Anyway, it would be great to see the surviving portion of a 1909 Piccadilly line gate end tube car that is at the LT Museum Acton Depot used as a basis for a CGI film simulating riding one of these carriages along the Piccadilly line... perhaps on a journey from Aldwych to Enfield West (sic), as at one time there were a few through trains that made this type of journey.