Conservatory Problem?

Spender£

I am in the process of having a glass Lean-to conservatory but we have encountered a problem, the left side load bearing wall still has old concrete footings which the neighbors conservatory floor base is attached to, the builders are worried that if they drill it out it might crack or cause problems in the neighbors floor or footings and so won't do it however, instead they said they must underpin the existing concrete instead which avoids the risk.
I wondered if this sounds right, i can understand that they could be liable if any damage was caused but would underpinning an existing foundation any good for this, if it is not then my options are limited:(.
The footing on my side were here before the neighbors conservatory but there builders have put the concrete up against my concrete footings which has joined them up so it seems.

Plantation7

There is such a thing as underpinning and it is undertaken for a variety of reasons including this, if they drill out the concreate and cause problems next door, they would be in strife for doing this and so are correct not to risk it, they would dig under the existing slab and fill with reinforced concreate to strengthen the existing footing. If this footing previously held the old wall then with underpinning it would become even stronger underneath.