I have a 1981 TR1 with a 750cc engine. Imported from japan. The carburetors ar behaving badly 'coughing' from the rear cylinder and will only start with a spray of easystart. Once running the engine runs with the coughing every now and then.
I haven't been able to locate a used set to replace them or a kit to refurbish them.
Does anyone have an idea what the problem may be or where to get some bits. I am based in London.

I think you just have to take the carburettors apart and clean then really good. Blow all the orifices with compressed air. Normally you dont have to replace anything. Probably it's some oxide in the float bowl that comes from some water in the petrol. If you are careful you don't have to by new gaskets either. Check the rubber-things between the carb and the cylinder head for leaks! see: http://www.xs11.com/faq/faqboots.shtml
Some parts as Float Bowl Gasket, and Float Needle and Seat are awailable. See for example; https://www.partsnmoreonline.com/PNMSite/XV%20Virago%2048-1412%20Carb%20rebuild%20kit.htm
Good luck!