I don't know if I'm left or right or centre. I kind of see myself as individual.
However regarding your question OP. Imo, especially without addressing the impact of mass immigration on less advantaged people and communities, mass immigration is a very right wing policy.
It's no different to the multiple threads we see on here when there's regional within-UK displaced 'blow ins'. People on those threads expressing concern about additional pressure on housing, jobs, and public services.
Regarding the argument about jobs needing filling. There's 916,000 job vacancies but over 1 million people on jobseekers benefits.
I've said it on other threads but I'll say it again. There is a minority of genuine bigots who 'don't like people not from here' (whether immigrant or regional within-UK 'blow-in'), however for most people it's legitimate concern about the impact especially on the less advantaged.
It isn't an easy subject to discuss as few want to encourage hate towards any particular group but the issues shouldn't be ignored. There should be adult and calm discussions and looking at solutions that are compassionate but also take into account the needs of people already here.
There's several options. Cutting immigration numbers, or more even spread across the country, or massive investment in social housing, public services, and job opportunities. Or a mix of those options. It's up to everyone to decide which they'd prefer.