Definitely sounds like dirt in the carburettor. Lots of threads in the carb section about this.
If you Google 'Weber Carburettor' there are several UK based specialists who will supply the rebuild kits. They come up on ebay as well. However the carb body really needs to go in one of those ultrasonic cleaning baths to get a guaranteed result, as there are so many small drillings that harbour dirt. A blow through with an airline might get it all out, but might not.
This has been an ongoing issue with my car and I'm coming round to a professional rebuild of the carburettor.
At the end of the day, Betas don't respond well to low usage. In my experience, the more mileage you do, the better they run.
Thanks Neil, good advice.
Cheers
Kev.