Given the title states that the route must be viable (which most clearly aren't), I'd like an alternative Bristol to Brighton service - but rather than the current one via Southampton, I'd like an extension of the North Downs route at both ends. It would give Brighton better links to Redhill, and better links between Gatwick and the West (i.e. no changes necessary). I think some 172s running this pattern would be ideal:
Bristol TM - Keynsham - Saltford - Oldfield Park - Bath Spa - Corsham - Chippenham - Swindon - Didcot Parkway - Reding - Wokingham - North Camp - Guildford - Dorking Deepdene - Reigate - Redhill - Gatwick Airport - Three Bridges - Haywards Heath - Brighton
(The local service west of Chippenham is intended to provide additional capacity on the Bath - Bristol corridor, and also a new station at Corsham without the need to make anything else go that way.)
Agreed. I don't think a Brighton-Manchester service would be at all far-fetched either. Maybe 1tph to each destination, with more frequent (and some express) services at peak times.
Aside from usage of the North Downs Line - a somewhat favourite subject with me

- I shall refine another of my proposals. Think of a line from somewhere in Essex to Reading, via a new Thames crossing, Bromley, East Croydon, Kingston and Heathrow.
This would have connections to an LU line (somewhere!), the DLR, direct Gatwick services, Tramlink and of course Heathrow Airport's various lines. There would be a junction South<->East at East Croydon. You'd have extra capacity on top of Crossrail, with the potential for services between the West Country and Wales, Reading & Heathrow and Norwich, Ipswich, Harwich and so on. With the South<->East junction, there would be potential for Portsmouth Harbour, Southampton, Brighton, Horsham, Gatwick and Redhill to East Anglia (etc.). I call this Crossrail 3.
An additional option for this route would be a link to the ELL (and other Overground lines at Dalston Junction) en-route, possibly with a North<->West junction at East Croydon.
A natural complementary route would be formed by a spur between North Camp on the North Downs Line and Heathrow Airport, thereby initiating Heathrow<->Gatwick services, with a double-track South<->West connection to the Crossrail 3 route. The North Downs Line would have to be quadrupled, possibly throughout, although initially only Redhill-Heathrow. Dorking Main and Dorking Deepdene should be joined with the old spur, as well as any further additions, with the stations combined, and two tracks of the line would have to be diverted to avoid useful but lightly-used stations such as Betchworth, Chilworth and Gomshall, some of which would need their buildings preserved. I have previously detailed potential solutions for remodelling Redhill station on other threads, and adding a new station under the A25 between Redhill and Reigate.