As promised, here is a report on our tree surgeons.
We have had our trees felled by a firm called "Forestall Sylvestre". They did a good job, including taking down some trees which were very close to the house and could not be "dropped". They were well-equipped, used all the appropriate safety gear, supplied proof of insurance, etc. They have a website and you can have a look at some of the work they have done. They are based in Tarragona and do work all over the province.