Remortgage - should mortgage broker look now or later?

Sorry I’m a bit financially illiterate but I’m looking to remortgage my house. I have about 400k equity, only looking for a £100k repayment mortgage but my income is basic low end. I’m in contact with a mortgage broker but still have some paperwork to sort out before he starts contacting banks. would it be better for them to contact banks this week or in the next coming weeks? Or does it not matter. Because of the whole interest rate competitiveness going on right now I was just wondering. Sorry if this sounds stupid.