Damage caused to my flat by neighbour above reconstructing his flat

The property has four floors in total and each floor has one flat. The floor above mine was bought by someone and that person started reconstructing and remodeling parts of the floor before moving in to the floor. The construction has caused damage to my property with minor and major cracks all across the floor (living room, bedrooms, bathrooms). The neighbor has agreed to get the repairs done, however, it seems he is just trying to do patch up work by putting plaster and painting over it rather than fixing actual damages to walls and cracks. We have got two people to provide quote on the charges for repairs but the neighbors says those are high and he will instead go with the person he chooses. In addition, neighbor says he can get the repair work done now but due to COVID delta variant situation, we are not willing to let laborers work in our floor as we are living in that place. My questions - Can we ask the neighbor to instead pay the money for repairs and we fix the damages once COVID risk is reduced? Our fear is that if we do not ask for the money now, he may say no at a later time or even sell his floor and leave. How do we agree on a quote which is agreeable to both parties? Can he force us to get the work done during COVID or refuse to get it done or pay later? Do you have any other advise on what can I do if he refuses to repair or pay? We have not yet taken any legal action because neighbor has been willing to repair.