How to potentially move a house sparrow nest / when

Hello, im new here. I have been regularly feeding the birds in my front garden for 3 years, i mostly attract House Sparrows, Robins, Blue tits and Wood Pigeons. Over the last year i've noticed a rattling noise coming from the corner roof of my extension. I assumed it was bushes rattling against the wall but today my husband went to investigate and found we have a gap between the felt roof and wall which what i think maybe a nesting site? (Photo attached) does this look like a nest? i've seen quite a few House Sparrows flying to and from the area so i think they may be going in there. My husband wants to now 'fix' the roof and gap but has promised he won't touch it until I can get advice on what the best thing to do is. I know ultimately we'll be disturbing the birds but is there a better time of the year to do it when they won't be using the area or nesting? I'm a bird lover and want to do as best as i can without causing them too much stress or damage....any advice please? Thank you!