If you do a tought program (Master) in a UK university, and then a PhD in the same place or lab, can you do 2 years of PhD instead of 3? Is it possible?

In the UK, a full-time taught masters will take 1 year, a full-time PhD will take approximately 3 years. So you should anticipate spending at least 4 years to complete a masters degree followed by a PhD.

In one of the universities I applied to, I was told that I could do a MA "by research" and immediately afterwards, start a PhD which might last only for 2 years (so I would have spent 3 years doing a MA + PhD). However I don't think this is common and anyway you would have to work very hard and do a good MA thesis to be able to convert it into a PhD thesis in 2 years.

Most universities will insist you are registered for three years min regardless of the Masters