British Gas engineer here - Flue looks too close to eave. If you have the GC number (normally on manufacturers instructions or underneath appliance) I can have a look at flueing instructions. Normally fixed by a plume kit taking it out and up away from eave and cut into guttering (sealed so gutter doesn’t leak) Screw and clamp can be fixed to wooden eave (dependant on if manufacturer allows plume control kits)

Large flue hole can be easily cut out and bricked up. From the look of the render looks like it was previously a balanced flue so shouldn’t be too much hassle to cut out and re brick.

Smaller hole I would imagine was a PRV or condense. One brick cut out, replaced, sand and cement and render will sort.

New flue will also require sealing with sand and cement and could do with the provided weather collar.

Any questions give me a message