Pruning Cherry Trees

Generally speaking, cherries and plums do not like to be pruned hard. Those long straggly branches should have been dealt with long ago, to avoid the need for such radical surgery in the future.

You're stuck with a difficult situation - you could prune it hard to get rid of the straggly bits, but the large wounds may never heal properly (not even if painted with wound sealant) and may become infected.
On the other hand, the tree is a straggly mess which is not going to get better unless you do something about it.

If it was my tree, I'd wait until next spring just as the buds start to swell and lop it back hard to restore the shape, but it may not fruit well for a year or two and will need follow-up pruning next spring and maybe summer to prevent it from simply re-growing lots more straggly branches. If you hack it back hard now, you will knock the stuffing out of it because it will lose so many of its leaves and hence not be able to gather energy to put into the winter reserves. If cut hard now, it could take many years to recover.
If pruned lightly, it won't make it any better shape.
If it was mine and I killed it through infection of the wounds, I'd not be too bothered given its condition. If it dies, I'd plant another and keep on top of the pruning to make sure it never got straggly. Fruit trees benefit from general tidying at least every two years, to avoid having to do difficult and life-theatening surgery at a later time.

Thanks for the info, I'll do that in the spring then. When you say wait for the buds to swell where would I then cut it? Near the buds?
We moved into the house with the tree in January so no idea when it was last pruned etc.

There is a section with diagrams in Harry Baker's book ISBN 0 85533 193 3. There are usually many of these books available for a few pence on Amazon

Make a sloped cut above a bud which you want to become the leader.
Many of the buds just below the topmost bud will become side branches.

Here are a couple of pictures of baby apple trees, which were just a 4-6ft single stem the previous winter, but which are branching nicely after heading-back by between one-third and one-half.

Note that after pruning, the topmost bud starts to grow out at a slight angle, but then more-or-less straightens to continue in a similar direction to which the branch/stem was heading before it was pruned.
The buds further down will spread out sideways at a much greater angle.

There is an exception, which is well demonstrated by: I have a rather difficult apple tree which has always wanted to grow one-sided.

In order to balance it, I have used heading cuts where the bud below the pruning cut heads upwards, which encourages a vigorous upright shoot to sprout, which helps to increase growth in that part of the tree.

Here's a picture of the difficult tree, with the unusual pruning cuts to stimulate strong upright shoots highlighted, plus also a red line indicating where I intend to make a thinning cut to remove an in-growing branch just below the strong leader:
Even so, you can still see how the rightmost side of the tree is thicker and stronger, but is gradually being balanced by a fast-growing left side:

Thanks for all your replies! You all rock!

Absolutely brilliantly informative post.