As others have said, you need to get it looked over by someone who knows classics. Someone on heres bound to be close to you, just to get an impartial opinion. It’s all too easy to get hung up on sentimentality etc and end up spending a hell of a lot of money fixing a car that’s got real issues! I know from experience!
Getting a few pics up on here will give you a few pointers too.
Don’t kid yourself about this type of work though. It IS expensive and it IS time consuming. You need to consider how suitable your car is to start with, then decide how far you want to go with it. Do you want something that runs and drives and looks nice? Reliable daily driver? Show winner? This too will determine what you’ll likely pay.
Don’t underestimate the cost of replacement parts either, your Triumph shouldn’t incur too much in the way of so called ‘scene tax’ so parts prices should be better than, say, Ford’s or Volkswagen’s etc. But, once you start pulling apart a car of this age it will get worse and you will find more and more problems as you go, hence - the costs are also likely to rise!
Paintwork. This also costs a lot nowadays for a quality job. You can get it cheap, but from experience it’s cheap for a reason! Don’t scrimp on it.
I know you said Coventry, but I’d seriously consider a much wider search radius. For the sake of hiring/borrowing a trailer and a bit of travelling you might get a better price and a better job. It’s worth thinking about.
If you do, I’ve had superb service and work done by this place. https://www.woodiesclassics.co.uk
He’s a small company, but very very good at what he does. Prices are very very competitive too. He did my Capri for me from a half repaired bare shell up to a fully repaired and painted shell with all the running gear back installed so it ‘rolls’ again. I’d highly recommend him.
He’s located near Chichester, down south though...
Also down here is this place. http://www.carcraftrestoration.co.uk
They specialise in classic car body and paint work, they did the metal work and paint on my Capri and their work is also second to none in my opinion.
As mentioned above, give TripleRich, a user on here, a PM. He does this for a living and his work is superb. Have a look at his mk1 Granada thread on here.
Likewise, JuridicalGrunt, I think he works at the same place? But his Rover SD1 resto thread is another great thread to have a look through.
Despite the warnings and costs etc though, it’s a great thing to do and you’ll have something really special at the end of it too.