UK Tier 2 (General) Switching Jobs Overlap

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Hi All,

I am currently on Tier 2 General Visa on company X. Company Y applied my Tier 2 General visa and it got approved. Situation is -
1) The CoS start date was 09/09/2019.
2) My application was approved on 27th Aug
3) I have not yet received my BRP card (The BRP had to be delivered on Company Y address but got delivered to my home address where i was not living anymore and was returned. This I got to know around 16/09/2019).
4) I am still working at Company X.
5) Company Y told me I need to join by 7/10/2019 since start date on CoS can be pushed by 28 days.
Currently, I am working in Company X. Is this legally fine? And If my last working day is 04/10/2019 in Company X, can I start working for Company Y on 7/10/2019