I have actually advised on the cause of your problem and gone into detail on it.
You originally asked if you should repair it or buy a new one.
If you feel you are able to , you can change the rear half of the tub, possibly an inner drum (you won't know if it's damaged until you get it out), and fit the parts that I detailed.
The cost will be higher than the British Gas offer though.
It wasn't a case of being quite obvious, it was a case of being very thorough and giving you all of the options.
I'm sorry that you feel you've only been told to call a repairer but if you go through the thread again you'll see I've taken you through the diagnostics, given you the cause of the problem and then given you the various options open to you.
The options are :-
Repair it yourself and the parts you'll need.
Have British Gas repair it for a fixed price.
Use the cost of repair against a new machine.
Do you want to do the work yourself?
If you do, let me know and I'll advise when you get stuck on the strip down.