If we want to fly to the West coast US from Manchester we would have to shutle down to the London airports. Do the shuttle airlines, probably BA, allow the Virgin baggage allowance on their flights?
No sorry, you have to stick to their luggage allowances as they are very unlikely to interline your bags onto your VS flights.
Saying that, BA do allow you 1 x 32Kg per adult for all domestic flights.
BD is a bit more restricted for weight but you are allowed 2 x 20Kg per adult on a 'Tiny' fare or as many as you like as long as they dont weight more than 20Kg on higher economy fares.
Regards