Starting new job while serving notice in old job

Hello,

My skilled worker visa has been switched from my current employer to my new employer. I have put in my notice. My current employer requires me to serve 3 months notice. However, I have about 4 weeks of paid holiday that I have accrued.

My question is, can I start my new job at the tail end of my notice period, when I am on 4 weeks paid leave, when I'm still technically serving out my notice period? From an immigration standpoint, is this permitted and will this have any impact on future settlement applications?

My current employer will not pursue me for breach of contract as i am not going to a competitor