In situations like this the more you try the worse it gets unless you have someone with the right equipment, who knows the cars, to work through the faults methodically. My suggestion is to get the car to Alfatune somehow. It sounds like the people who have worked on the car do not have the neccessary level of expertise for whatever reason.
Its all very well us trying to guess the problem, but too many things have been done now to make much sense. I can't for the life of me understand the battery change, unless it was proven that the old battery was faulty.
The fault could be a number of things, but a good session on a diagnostic machine with a skilled operator will most likely pin point the fault and save time and money.
I'm sorry I can't give more definite advice, except to be very careful about who you let work on an Alfa. We see it time and time again when people who don't know the cars cost owners a lot of wasted time and money, and give the cars an undeserved bad reputation along the way.
Is Keighley any closer to Blackburn? there is Perseverance Garage (Formerly CW Lear) Alfa Specialists. It has a very good reputation under Wyn, who has retired, but his assistant now has the business, so hopefully the good work continues