we keep getting birds in the loft, and they nest there over spring/summer.

I presume you are talking about the gap between the fascia and the bottom of the first row of tiles.if so,you can get something called eaves comb fillers.these are fixed (usually nailed) on to the top of the fascia and create a barrier but are designed to still allow airflow.they are very easily inserted and can be done by a builder,roofer,or handyman as they only require the first row of tiles to be pushed back temporarily.this is an easy job and should not take long or cost much.

yes ,get the roof sealed properly to the walls at the side

Depending on the roof type you can fit netting over the access points, or fit vented sofits. However, before you do you must check that there are no birds inside, and make doubly sure that there are no bats as they are a protected species and the penalties for disturbing them are quite severe.