Hi,
I am PhDing at IC, and my project involves one big industrial partner.
I am paid 1041pounds per month and read that the majority of PhD in London are funded more (additionnal £2000 in London, industrial topup).

I am 100% sure that no one involved in my project knows anything about that as:
my supervisor had no idea of my project before hiring me
he ask me first to pay for the tution fees(I come from the EU)
he doesn't know how much I am paid!
Is there anyway to clarify my situation?

If I were you I would enquire with the postgraduate office at your Uni. I'm sure they will know whether you are being paid the correct amount or otherwise. Best wishes.

Usually research council funded studentships are available to UK and EU students, however the EU students grant is for fees only and does not include funds for living (rent, food, travel, etc). It may be that your industrial partner's contribution is allowing you to be paid the 1000 per month.

Check with the international and/or postgraduate offices at imperial college or ask your grant awarding body for a copy of the terms and conditions of your grant.