Tree advice

Ectophile

In the short term, the trees will look a bit weird, with clumps of leaves growing around each of the cut ends.

If the work was done right, these clumps will gradually expand into twigs, then branches, and the trees should start to look normal again.

Mistral001

koalakoala said:

They look far too close to neighbouring properties, roots can cause so much damage

A survey of the walls facing the garden might be necessary in order to determine whether there are any signs of damage to them.  Note complete removal of the trees, under some circumstances can cause swelling in the sub-soil due to removal of water take-up from roots.  This has been known to cause  damage foundations, so get advice before doing this even though you find that a survey shows  there are no signs of damage to the neighbouring walls at present.

Section62

luke1066_2 said:

My question is what will these trees look like once they start new growth?

what type of pruning is it that these two have received. 

"Crown Reduction"

If it has been done by a professional you should get new growth appearing at the cut ends of the branches, which will in time (say two to three years) give you a nice 'tree' shape.

In terms of the foundations of the neighbouring property I would be far more concerend about the sudden removal of the trees rather than their growth.  Removal of trees of that size really ought to be done over a period of time, e.g. two or three crown reductions followed by eventual removal.

Check very carefully before having further work done on them - don't rely on what the vendor says, and don't rely on the searches.  Both can be wrong.