To give you an idea, my inlaws recently purchased a '73 Coupe which had 22K original miles. It had receipts for many thousands of dollars of work in the last couple years.
Beyond the purchase price, they're already in multiple thousand dollars and haven't cracked open the engine, (except for a transmission seat and a few easy access gaskets up top.)
Series III parts are not that expensive -- when compared to, say, enriched uranium or a MLB franchise. Compared to Triumph, Chevy or Ford parts, they are expensive and hard to find. (Look at the cost of a piston and multiply by twelve...then go try to find a voltage regulator!)
If the car needs new interior, top, paint, brakes...and it hasn't run, it most likely needs new gaskets throughout the engine, as well as rear-end. It also needs new hoses. Figure you're also in for four Stromberg 175CD rebuild kits.
A real "frame-off" resto on one of these cars -CAN- be done for $40K, but since a paint job commensurate with the type of car should cost$4-6K minimum, and there are so many other expensive parts and possible gremlins to work out - for the overall quality, you're probably looking at $60K minimum for a show-car result.
A regional show-winner caliber XKE Series III carries a value of $52,500, with a normal local-show quality car around $30Kish. A national concours car will be $75K, but you'll spend $100K+ creating this car.
And the largest problem: finding someone to work on these cars. Even European car specialists tend to botch work on V12 Jags (at least that's what we've seen here, and heard from other owners.)
Which is why it always makes sense to buy someone else's frame-off resto.
But if you can get the car for next to nothing (like, say, $5,000,) it might be worth "the risk," and see if you can get it going cheaply.