Tax implications are basd on your tax residency. This is determined by the guidelines here:
RDR3 Statutory Residence Test
One example is if you are in the UK for more than 183 days then you would be a UK tax resident and worldwide income would be reportable to the UK.
With regards to employer rules in terms of how they deduct Tax and NI, this would need to be referred to the Employers helpline:
Employers: general enquiries